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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises use substitution and partial fractions to find the indefinite integral. sec² x tan x(tan x + 1) dx
In Exercises use integration tables to find the indefinite integral. In x x(3 + 2 In x) dx
In Exercises use substitution and partial fractions to find the indefinite integral. S ex (ex - 1)(ex + 4) dx
In Exercises use integration tables to find the indefinite integral. 1 x² √2 + 9x² dx
In Exercises use substitution and partial fractions to find the indefinite integral. S sec² x tan²x + 5 tan x + 6 dx
In Exercises use substitution and partial fractions to find the indefinite integral. I ex (e²x + 1)(ex - 1) dx
In Exercises use integration tables to find the indefinite integral. (x² - 6x +10)² dx
In Exercises use substitution and partial fractions to find the indefinite integral. √x x - 4 S dx
In Exercises use integration tables to find the indefinite integral. et (1-e²x)3/2 dx
In Exercises use integration tables to find the indefinite integral. X /x46x² + 5 dx
In Exercises use integration tables to find the indefinite integral. 5-x √√√√5 = = = d dx + x
In Exercises use substitution and partial fractions to find the indefinite integral. 1 √x - 3√/x
In Exercises use the method of partial fractions to verify the integration formula. 1 x(a + bx) dx = 1 In a X a + bx + C
In Exercises use integration tables to find the indefinite integral. J cos x /sin²x + 1dx
In Exercises use integration tables to find the indefinite integral. cot 0 de
In Exercises use the method of partial fractions to verify the integration formula. 1 1 a √ ₁ ² ² ² √²d²x = 2/₁ ²/² + x + ₁ In C 2 - 2a |a - X
In Exercises use the method of partial fractions to verify the integration formula. 1 x²(a + bx) dx 1 ax - ++ C (a + bx In
In Exercises use integration tables to find the indefinite integral. e3x (1 + ex)³ dx
In Exercises use the method of partial fractions to verify the integration formula. S X (a + bx)² dx = 1 a b²a + bx x1) + + In|a + bx| + C
In Exercises use integration tables to evaluate the definite integral. 10 x /3 + 2x dx
In Exercises use integration tables to evaluate the definite integral. S xex dx Jo
What is the first step when integratingExplain. x3 x-5 dx?
In Exercises use integration tables to evaluate the definite integral. TT/2 0 x sin 2x dx
In Exercises use integration tables to evaluate the definite integral. In x dx
State the method you would use to evaluate each integral. Explain why you chose that method. Do not integrate.(a)(b)(c) x + 1 x² + 2x - 8 dx
Use the graph of ƒ' shown in the figure to answer the following.(a) Is ƒ(3) - ƒ(2) > 0? Explain.(b) Which is greater, the area under the graph of ƒ' from 1 to 2, or the area under the graph of
In Exercises use integration tables to evaluate the definite integral. π/2 J-7/2 cos x - dx 1 + sin² x
Describe the decomposition of the proper rational function N(x)/D(x) (a) For D(x) = (px + q)m(b) For D(x) = (ax² + bx + c)n where ax² + bx + c is irreducible. Explain why you chose that method.
In Exercises use integration tables to evaluate the definite integral. x2 (5 + 2x)² xp.
Find the area of the region bounded by the graphs of y = 12/(x² + 5x + 6), y = 0, x = 0, and x = 1.
The predicted cost C (in hundreds of thousands of dollars) for a company to remove p% of a chemical from its waste water is shown in the table.A model for the data is given byfor 0 ≤ p < 100.
In Exercises use integration tables to evaluate the definite integral. (3 x/ √x² + 16 dx
In Exercises use integration tables to evaluate the definite integral. π/2 Jo t³ cos t dt
Consider the region bounded by the graph ofon the interval [0, 1] Find the volume of the solid generated by revolving this region about the x-axis. न 2 || (2 - x)² 2 (1 + x)²
In Exercises verify the integration formula. u² (a + bu)² du = 1/(bu a² a + bu 2a Inja + bul) + C
A single infected individual enters a community of n susceptible individuals. Let x be the number of newly infected individuals at time t. The common epidemic model assumes that the disease spreads
Find the area of the region bounded by the graphs of y = 7/(16 - x²) and y = 1.
In Exercises verify the integration formula. June - n fun-1 sin u du un cos u du = u" sin un
In Exercises verify the integration formula. 2 [√at bu du = (2n ²4 116(² √a + bu - nabudu) + + 1)b +
In Exercises verify the integration formula. arctan u du = u = u arctan arctan u u — In 1 + a + C
In Exercises verify the integration formula. 1 (u² + a²)3/2 du tu a²√√u² ± a² + C
In Exercises find or evaluate the integral. 1 2 - 3 sin Ꮎ dᎾ
Consider the region bounded by the graphs of y = 2x/(x² + 1), y = 0, x = 0, and x = 3. Find the volume of the solid generated by revolving the region about the x-axis. Find the centroid of the
Evaluatein two different ways, one of which is partial fractions. Jo X 1 + x4 dx
In Exercises verify the integration formula. [ (In u)" du = u(In u)" - nf (In uyª-1 du
in two different ways, one of which is partial fractions.Prove 22 7 = [₁ ²² 0 ㅠ= x*(1-x)4 1 + x² dx.
In Exercises find or evaluate the integral. J sin 0 1 + cos²0 de
In Exercises find or evaluate the integral. *π/2 10 1 1+ sin + cos 0 de
In Exercises find or evaluate the integral. TT/2 1 3-2 cos 0 de
In Exercises find or evaluate the integral. sin 0 32 cos 0 do
In Exercises find the area of the region bounded by the graphs of the equations. y= X √x +3° y = 0, x = 6
In Exercises find or evaluate the integral. cos ( 1 + cos 0 : dᎾ
In Exercises find or evaluate the integral. sin √√ √e do
In Exercises find or evaluate the integral. 4 csc cot 0 to do
Use the graph of ƒ' shown in the figure to answer the following.(a) Approximate the slope of ƒ at x = -1. Explain.(b) Approximate any open intervals in which the graph of ƒ is increasing and any
In Exercises find the area of the region bounded by the graphs of the equations. y = x 0, 1 + x²y = 0₁ x = 2 et
Repeat Exercise 69, usingpounds.Data from in Exercise 69A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet (0 ≤ x ≤ 5), where the variable force required is
(a) Evaluate ƒxn In x dx for n = 1, 2, and 3. Describe any patterns you notice.(b) Write a general rule for evaluating the integral in part(a), for an integer n ≥ 1.
Describe what is meant by a reduction formula. Give an example.
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.To use a table of integrals, the integral you are evaluating must
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.When using a table of integrals, you may have to make
A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet (0 ≤ x ≤ 5), where the variable force required is F(x) = 2000xe-x pounds. Find the work done in pushing the
Consider the region bounded by the graphs ofFind the volume of the solid generated by revolving the region about the y-axis. y=x√16x², y = 0, x = 0, and x = 4.
In Exercises use partial fractions to find the indefinite integral. X 16x4 - 1 dx
In Exercises use partial fractions to find the indefinite integral. x² x42x² 8 dx
In Exercises use partial fractions to find the indefinite integral. 8x x³ + x² - x - 1 dx
In Exercises use partial fractions to find the indefinite integral. x² + 3x - 4 x³ 4x² + 4x - dx
In Exercises use partial fractions to find the indefinite integral. x² - 1 x³ + x dx
In Exercises use partial fractions to find the indefinite integral. S 5x – 2 (x - 2)² dx
In Exercises use partial fractions to find the indefinite integral. x² - 1 x³ + x dx
In Exercises use partial fractions to find the indefinite integral. 4x² + 2x - x³ + x² 1 dx
In Exercises use partial fractions to find the indefinite integral. x + 2 r+5r dx
In Exercises use partial fractions to find the indefinite integral. 3-x 3x²2 2x1 S dx
In Exercises use partial fractions to find the indefinite integral. 2x3 4x² 15x + 5 x²2x8 - dx
In Exercises use partial fractions to find the indefinite integral. x3 x + 3 - x² + x = 2 dx
In Exercises use partial fractions to find the indefinite integral. x² + 12x + 12 x² - 4x dx
In Exercises use partial fractions to find the indefinite integral. 1 x² - 9 dx
In Exercises use partial fractions to find the indefinite integral. 5 x² + 3x - 4 - dx
In Exercises use partial fractions to find the indefinite integral. 2 9x² - 1 dx
In Exercises write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 2x - 1 x(x² + 1)²
In Exercises write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 2x - 3 x³ + 10x
In Exercises write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 2x² + 1 (x − 3)³
In Exercises write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. x² 4 8x
In Exercises find the area of the region bounded by the graphs of the equations. y = cos² x, y = sin² x, x X = πT 4' X t 4
In Exercises use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral.Data from in Theorem 8.2 THEOREM 8.2 Special Integration Formulas (a > 0) 1. 1. S√α² - 1² du
In Exercises find the indefinite integral using the substitution x = 5 sec θ. 1 x² - 25 dx
The following sum is a finite Fourier series.(a) Use Exercise 89 to show that the th coefficient an is given by(b)Data from in Exercise 89The inner product of two functions ƒ and g on [a, b] is
In Exercises use the results find the integral. sin sin4 x cos² x dx
The inner product of two functions ƒ and g on [a, b] is given byTwo distinct functions ƒ and g are said to be orthogonal if〈ƒ, g〉= 0. Show that the following set of functions is orthogonal on
Use the result of Exercise 80 to prove the following versions of Wallis’s Formulas.If n is odd (n ≥ 3), thenIf n is even (n ≥ 2), thenData from in Exercise 80The table shows the normal maximum
The table shows the normal maximum (high) and minimum (low) temperatures (in degrees Fahrenheit) in Erie, Pennsylvania, for each month of the year.The maximum and minimum temperatures can be modeled
In Exercises use the results find the integral. [sec4 (2mx/5) dx
In Exercises use the results find the integral. [cos4 x dx
In Exercises use the results find the integral. sin sin5 x dx
In Exercises use integration by parts to verify the reduction formula. Ss sec" x dx = 1 n- 1 sec 2 x tan x + n n 2 뤼 1 - sec-2 x dx
In Exercises use integration by parts to verify the reduction formula. S cos" x dx = "="f₁ n cos"- ¹ x sin x n + n cos"-2 x dx
In Exercises use integration by parts to verify the reduction formula. S sin" x dx = sin x cos x n + "=¹ | ₁ n sin"-2x dx
In Exercises for the region bounded by the graphs of the equations, find (a) The volume of the solid formed by revolving the region about the x-axis and (b) The centroid of the region.
In Exercises use integration by parts to verify the reduction formula. Ja cosm x sin" x dx = cosm+1 x sinn-1 x m+n S 1 n m + n + cosm x sinn-2 x dx
In Exercises for the region bounded by the graphs of the equations, find (a) The volume of the solid formed by revolving the region about the x-axis and (b) The centroid of the region. y =

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