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mathematics
precalculus

Questions and Answers of Precalculus

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. e/x аз .3 -1 X |-1
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. *m/2 Cos 0 -de Jo /sin 0
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. r In r dr
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. *4 dx Jo x² х2 — х — 2
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. 'T/2 tan20 d0
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. '5 dw lo w – 2
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. 1 dx Ух — 1
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. dx /1 – x²
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. •3 1 -dx -2 X x*
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. - dx (x + 1)?
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. dx *14 -2 Vx + 2
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. *5 -dp- Jo 3.
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. -dx ах о х J0
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. dx Vx + xVx
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. Le dy
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. 1. (In Je x(In x)?
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. - dz z4 + 4
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. In x -dx ах х /1
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. In x dx .2
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. ye J2 уе У dy Уе 3у
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. Г.- ze 2z dz -00
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. dv ,2 v? + 2v – 3
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. -dx + x .2
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. sin0 ecose de
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. sin'a da S: 11
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. -1/x dx x? oo
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. хе** dx 2. -00
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. (у — Зу?) dy
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. x² -dxp /1 + x3
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. 2' dr
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. -Sp dp 12
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. (2x + 1)3
Determine whether each integral is convergent or divergent. Evaluate those that are convergent. 1 = dx V1 + x
Which of the following integrals are improper? Why?(a)(b)(c)(d) T/4 tan x dx tan x dx
Show that 1/3 (Tn + 2/3Mn) S2n.
Show that if f is a polynomial of degree 3 or lower, then Simpson’s Rule gives the exact value of ∫ba f(x) dx .
Sketch the graph of a continuous function on [0, 2] for which the right endpoint approximation with n = 2 is more accurate than Simpson’s Rule.
The region bounded by the curve y = 1/(1 + e-x), the x and y-axes, and the line x = 10 is rotated about the x-axis. Use Simpson’s Rule with n = 10 to estimate the volume of the resulting solid.
A graph of the temperature in Boston on August 11, 2013, is shown. Use Simpson’s Rule with n = 12 to estimate the average temperature on that day. TA (F) 80- 70 60 4 8 noon 4)
(a) A table of values of a function t is given. Use Simpson’s Rule to estimate (b) Ifestimate the error involved in the approximation in part (a). dx. *1.6 g(x) g(x) х х 0.0 12.1 1.0 12.2
Estimate the area under the graph in the figure by using (a) The Trapezoidal Rule, (b) The Midpoint Rule, and (c) Simpson’s Rule, each with n = 6. yA 1 2 3 6 х 4 5
Find the approximations Tn, Mn, and Sn for n = 6 and 12. Then compute the corresponding errors ET, EM, and ES. (Round your answers to six decimal places. You may wish to use the sum command on a
Find the approximations Ln, Rn, Tn, and Mn for n = 5, 10, and 20. Then compute the corresponding errors EL, ER, ET, and EM. (Round your answers to six decimal places. You may wish to use the sum
Use(a) The Trapezoidal Rule, (b) The Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) I
Use (a) The Trapezoidal Rule,(b) The Midpoint Rule, and(c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) '4 In(1 +
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) (3 sin t dt,
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) x2 dx, п
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) dt, n = 10 2
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) Vy cos y dy,
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) | ell# dx,
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) '4 sin x dx,
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) п/2 V1 +
Use (a) The Trapezoidal Rule, (b) The Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal
Use (a) The Trapezoidal Rule, (b) The Midpoint Rule, and(c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) r2
Use (a) The Trapezoidal Rule, (b) The Midpoint Rule, (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
Use (a) The Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) Compare your results to the actual
Use(a) The Midpoint Rule and (b) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) Compare your results to the actual
Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. V1 + E
Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. SxVT=x² dx
Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. cos*x dx
Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. cos*x dx
Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. (xV? + 4 d + 4 dx -2
Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. cscx dx
Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. dx sec'x
Verify Formula 31(a) By differentiation and (b) By substituting u = a sin θ.
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. sec?0 tan?0 de 9 – tan20
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. x*dx x10 - 2
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. – 3) dt |e ´sin(æt
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. | Ve2x – 1 dx
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. dx 2x
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. cos- (x-2) х3
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. -× dx x*e-* dx
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. V4 + (In x)²
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. |x*) dx arcsin(x²
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. | sec'x dx
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. 22 x'/4x? – x* dx +3
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. e* dx 3 – e2x
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. sin 20 de 5 – sin 0
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. sin?x cos x In(sin x) dx
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. dx 2x3 Зx2
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. |y/6 + 4y – 4y² dy
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. 3t dt Ve2t – 1
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. coth(1/y) -dy y?
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. x' sinx dx х
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. arctan Vx dx
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. 2 + xª dx
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. TT cos'0 de
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. V2y? – 3 dy y?
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. /9x² + 4 dx .2
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. et dx 4 - e2x
Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. x?V4 — х? dx '2
Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral. entry 69 . tan (πΧ/6 d; ν0
Use the indicated entry in the Table of Integrals on the Reference Pages to evaluate the integral. entry 113 I Vx - x² dx; Jo
We know that
Evaluate the integral. sin x cos X dx .4 sin*x + cos*x
Evaluate the integral. | VI - sin x dx
Evaluate the integral. sec x сos 2х -dx sin x + sec x
Evaluate the integral. x sin?x cos x dx
Evaluate the integral. 1 + sin x 1- sin x

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