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Chapter 6: Q. 68 (page 540)

Set up and solve a definite integral to find the exact area of each surface of revolution obtained by revolving the curve $y = f (x)$ around the x-axis on the interval [a, b].
$f (x) = e^{- x}, [a, b] = [- 1, 1]$

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Most popular questions from this chapter

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29–52.

34. $\frac{d y}{d x} = \frac{1}{y}, y (0) = 3$

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.

$\frac{d y}{d x} = x y^{2}$

Explain in your own words how the slopes of the line segments in a slope field for a differential equation are related to the differential equation.

find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0).

$\frac{d y}{d x} = \frac{x}{y}$

Find the exact value of the arc length of each function f (x) on [a, b] by writing the arc length as a definite integral and then solving that integral.

$f (x) = 3 x + 1, [a, b] = [- 1, 4]$

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Set up and solve a definite integral to find the exact area of each surface of revolution obtained by revolving the curve $y = f (x)$ around the x-axis on the interval [a, b].
$f (x) = e^{- x}, [a, b] = [- 1, 1]$

Short Answer

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Step 1. Given Information

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Set up and solve a definite integral to find the exact area of each surface of revolution obtained by revolving the curve y=f(x)around the x-axis on the interval [a, b]. f(x)=e−x,[a,b]=[−1,1]

Short Answer

Step by step solution

Step 1. Given Information

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Set up and solve a definite integral to find the exact area of each surface of revolution obtained by revolving the curve $y = f (x)$ around the x-axis on the interval [a, b].
$f (x) = e^{- x}, [a, b] = [- 1, 1]$