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Chapter 6: Q. 47 (page 512)

Consider the region between the graphs of $f (x) = x^{2}$ and $g (x) = 2 x$ on $[0, 2]$ .For each line of rotation given in Exercises 47鈥�50, use definite integrals to find the volume of the resulting solid.

Short Answer

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The volume of the solid is

Step by step solution

Step 1. Given Information

The given figure is

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Most popular questions from this chapter

Consider the region between the graph of $f (x) = \frac{3}{x}$ and the x-axis on [1,3]. For each line of rotation given in Exercises 31鈥� 34, use definite integrals to find the volume of the resulting solid.

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

$\frac{d y}{d x} = 10 - 7 y, y (0) = \frac{1}{11}$

Approximate the arc length of f (x) on [a, b], using n line segments and the distance formula. Include a sketch of f (x) and the line segments .

$f (x) = x^{3}, [a, b] = [- 2, 2], n = 4$

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

$\frac{d y}{d x} = \sqrt{4 y}, y (1) = 1$

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

$\frac{d y}{d x} = \frac{x + 1}{\sqrt{x}}$

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Consider the region between the graphs offx=x2and gx=2xon 0,2.For each line of rotation given in Exercises 47鈥�50, use definite integrals to find the volume of the resulting solid.

Short Answer

Step by step solution

Step 1. Given Information

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Consider the region between the graphs of $f (x) = x^{2}$ and $g (x) = 2 x$ on $[0, 2]$ .For each line of rotation given in Exercises 47鈥�50, use definite integrals to find the volume of the resulting solid.