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mathematics
calculus 4th

Questions and Answers of Calculus 4th

(a) Compute the area under the graph of y = sinh x for 0 ≤ x ≤ 5.(b) Compute the area under the graph of y = sinh−1 x for 0 ≤ x ≤ sinh 5.(c) Show that the sum of the areas in (a) and (b) is
(a) Compute the area under the graph of y = tanh x for 0 ≤ x ≤ 4.(b) Compute the area under the graph of y = tanh−1 x for 0 ≤ x ≤ tanh 4.(c) Show that the sum of the areas in (a) and (b)
Show that if u = tanh(x/2), thenFor the first relation, use the identities cosh x = 1+u² 1-4²⁹ sinh x = 2u 1-u²⁹ dx = 2du 1- u²
Evaluate using the substitution of Exercise 43.Data From Exercise 43Show that if u = tanh(x/2), thenFor the first relation, use the identities Ss sech x dx
Evaluate using the substitution of Exercise 43.Data From Exercise 43Show that if u = tanh(x/2), thenFor the first relation, use the identities dx 1 + cosh x S
Evaluate using the substitution of Exercise 43.Data From Exercise 43Show that if u = tanh(x/2), thenFor the first relation, use the identities S dx 1 - cosh x
Refer to the function gd(y) = tan−1(sinh y), called the Gudermannian. In a map of the earth constructed by Mercator projection, points located y radial units from the equator correspond to points
Refer to the function gd(y) = tan−1(sinh y), called the Gudermannian. In a map of the earth constructed by Mercator projection, points located y radial units from the equator correspond to points
Refer to the function gd(y) = tan−1(sinh y), called the Gudermannian. In a map of the earth constructed by Mercator projection, points located y radial units from the equator correspond to points
Refer to the function gd(y) = tan−1(sinh y), called the Gudermannian. In a map of the earth constructed by Mercator projection, points located y radial units from the equator correspond to points
Calculate the integral in terms of the inverse hyperbolic functions. dx √x²1 s
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are substitution (specify u and du), Integration by Parts (specify u and dv), a trigonometric method, or
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Match the rational functions (a)–(d) with the corresponding partial fraction decompositions (i)–(iv). (a) (b) (c) (d) (ii) x² + 4x + 12 (x + 2)(x² + 4) 2x² + 8x + 24 (iii) (x + 2)²(x² +
Evaluate the integral using the appropriate method or combination of methods covered thus far in the text. You may use the integral tables at the end of the text, but do not use a computer algebra
Clear the denominators in the following partial fraction decomposition and determine the constant B (substitute a value of x or use the method of undetermined coefficients). 3x² + 11x + 12 (x + 1)(x
Find the constants in the partial fraction decomposition 2x + 4 (x - 2)(x2 + 4) A x-2 + Bx + C x² + 4
Evaluate using long division first to write ƒ(x) as the sum of a polynomial and a proper rational function. x dx 3x-4 S
Evaluate using long division first to write ƒ(x) as the sum of a polynomial and a proper rational function. *(x² + 2) dx x + 3 Se
Evaluate using long division first to write ƒ(x) as the sum of a polynomial and a proper rational function. (x³ + 2x² + 1) dx x + 2
Evaluate using long division first to write ƒ(x) as the sum of a polynomial and a proper rational function. (x³ + 1) dx x² + 1
Evaluate by using first substitution and then partial fractions if necessary. S ex dx e2x - 1
Evaluate by using first substitution and then partial fractions if necessary. sec2 Ꮎ dᎾ tan²01 S
Evaluate ∫ √x dx/x − 1. Use the substitution u = √x (sometimes called a rationalizing substitution).
Evaluate ∫ dx/x1/2 − x1/3 .Use the substitution u = x1/6.
Evaluate ∫ dx/x5/4 − 4x3/4 .
Evaluate ∫ dx/x4/3 + x − 2x2/3.
Show that the substitution θ = 2 tan−1 t (Figure 2) yields the formulasThis substitution transforms the integral of any rational function of cos θ and sin θ into an integral of a rational
Evaluate ∫ dx/x2 − 1 in two ways: using partial fractions and using trigonometric substitution. Verify that the two answers agree.
Graph the equation (x − 40)y2 = 10x(x − 30) and find the volume of the solid obtained by revolving a the region between the graph and the x-axis for 0 ≤ x ≤ 30 around the x-axis.
Use the substitution of Exercise 57 to evaluate ∫dθ/cos θ + sin θ.Data From Exercise 57Show that the substitution θ = 2 tan−1 t (Figure 2) yields the formulasThis substitution transforms the
Suppose that Q(x) = (x − a)(x − b), where a ≠ b, and let P/Q be a proper rational function so that(a) Show that (b) Use this result to find the partial fraction decomposition for P(x) = 3x −
Prove the general formulawhere a, b are constants such that a ≠ b. dx (x-a)(x - b) S 1 In a-b x-al + C x-b|
Find the volume of the solid of revolution that results when the region under the graph of ƒ(x) = x √sin x for 0 ≤ x ≤ π is revolved around the x-axis.
Find the volume of the solid of revolution that results when the region under the graph of ƒ(x) = ln x for 1 ≤ x ≤ e is revolved around the x-axis.
Find the volume of the solid of revolution that results when the region under the graph of ƒ(x) = 3 sin x for 0 ≤ x ≤ π is revolved around the y-axis.
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are algebraic manipulation, substitution (specify u and du), and Integration by Parts (specify u and dv). If it
Find the volume of the solid of revolution that results when the region under the graph of ƒ(x) = e−x for 0 ≤ x ≤ 1 is revolved around:(a) The y-axis.(b) The line x = 1.
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are algebraic manipulation, substitution (specify u and du), and Integration by Parts (specify u and dv). If it
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are algebraic manipulation, substitution (specify u and du), and Integration by Parts (specify u and dv). If it
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are algebraic manipulation, substitution (specify u and du), and Integration by Parts (specify u and dv). If it
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are algebraic manipulation, substitution (specify u and du), and Integration by Parts (specify u and dv). If it
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are algebraic manipulation, substitution (specify u and du), and Integration by Parts (specify u and dv). If it

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