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Exam 5: Integrals

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Exam 1: Functions and Models160 Questionsadd course
Exam 2: Limits and Derivatives160 Questionsadd course
Exam 3: Differentiation Rules160 Questionsadd course
Exam 4: Applications of Differentiation159 Questionsadd course
Exam 5: Integrals160 Questionsadd course
Exam 6: Applications of Integration160 Questionsadd course
Exam 7: Techniques of Integration160 Questionsadd course
Exam 8: Further Applications of Integration160 Questionsadd course
Exam 9: Differential Equations160 Questionsadd course
Exam 10: Parametric Equations and Polar Coordinates160 Questionsadd course
Exam 11: Infinite Sequences and Series160 Questionsadd course
Exam 12: Vectors and the Geometry of Space159 Questionsadd course
Exam 13: Vector Functions160 Questionsadd course
Exam 14: Partial Derivatives158 Questionsadd course
Exam 15: Multiple Integrals160 Questionsadd course
Exam 16: Vector Calculus160 Questionsadd course
Exam 17: Second-Order Differential Equations160 Questionsadd course
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Find the integral using the indicated substitution. Find the integral using the indicated substitution.

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Question 1
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Evaluate the integral. Evaluate the integral.

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Question 2
Correct Answer:
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Find the integral using an appropriate trigonometric substitution.Select the correct Answer Find the integral using an appropriate trigonometric substitution.Select the correct Answer

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Question 3
Correct Answer:
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B

Find the indefinite integral. Find the indefinite integral.

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Question 4

Find a function (x) such that Find a function (x) such that for and some number . for Find a function (x) such that for and some number . and some number . Find a function (x) such that for and some number . Find a function (x) such that for and some number .

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Question 5

Find the area of the region that lies to the right of the y-axis and to the left of the parabola Find the area of the region that lies to the right of the y-axis and to the left of the parabola

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Question 6

Select the correct Answer: for each question. -Find the indefinite integral Select the correct Answer: for each question. -Find the indefinite integral

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Question 7

Evaluate the integral.Select the correct Answer Evaluate the integral.Select the correct Answer

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Question 8

a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, a.Use Part 1 of the Fundamental Theorem of Calculus to find a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, b.Use Part 2 of the Fundamental Theorem of Calculus to integrate a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, to obtain an alternative expression for a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, c.Differentiate the expression for a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, found in part (b).The Fundamental Theorem of Calculus, Part 1 If a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, is continuous on [ a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, then the function a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, defined by a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, is differentiable on a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, and a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, The Fundamental Theorem of Calculus, Part 2 If a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, is continuous on a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, then a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, where a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, is any antiderivative of that is, a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is, a.Use Part 1 of the Fundamental Theorem of Calculus to find b.Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an alternative expression for c.Differentiate the expression for found in part (b).The Fundamental Theorem of Calculus, Part 1 If is continuous on [ then the function defined by is differentiable on and The Fundamental Theorem of Calculus, Part 2 If is continuous on then where is any antiderivative of that is,

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Question 9

Evaluate the definite integral. Evaluate the definite integral.

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Question 10

If If is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years and is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years If is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years and and If is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years and

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Question 11

Evaluate the integral. Evaluate the integral.

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Question 12

Find the integral. Find the integral.

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Question 13

Evaluate the indefinite integral. Evaluate the indefinite integral.

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Question 14

By reading values from the given graph of By reading values from the given graph of use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of By reading values from the given graph of use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of By reading values from the given graph of use five rectangles to find a lower estimate, to the nearest whole number, for the area from 0 to 10 under the given graph of

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Question 15

Find the general indefinite integral.Select the correct Answer Find the general indefinite integral.Select the correct Answer

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Question 16

If If where where If where

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Question 17

Select the correct Answer: for each question. -Find the integral. Select the correct Answer: for each question. -Find the integral.

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Question 18

Select the correct Answer: for each question. -The area of the region that lies to the right of the y-axis and to the left of the parabola Select the correct Answer: for each question. -The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral Find the area.. (the shaded region in the figure) is given by the integral Select the correct Answer: for each question. -The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral Find the area.. Find the area.. Select the correct Answer: for each question. -The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the integral Find the area..

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Question 19

Select the correct Answer for each question. -Use the following property of the definite integral to estimate the definite integral Select the correct Answer for each question. -Use the following property of the definite integral to estimate the definite integral Select the correct Answer for each question. -Use the following property of the definite integral to estimate the definite integral

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Question 20
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