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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 47–50, use definite integrals to find the volume of the resulting solid.

Short Answer

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The volume of the solid is

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Step 1. Given Information

The given figure is

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

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For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals

$π \int_{0}^{\frac{π}{2}} \cos^{2} (x) d x a n d π \int_{\frac{π}{2}}^{π} \cos^{2} (x) d x$

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