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Chapter 13: Q. 38 (page 1015)

In Exercises 35鈥�40, find the volume of the solid bounded above by the given function over the specified region惟={x,y|0鈮�x鈮�蟺4andsinx鈮�y鈮�cosx}f(x,y)=x2y.

Short Answer

Expert verified

Volume bounded by given function is:蟺2-864

Step by step solution

01

Step 1. Given Information

Function,f(x,y)=x2y

Region,惟={x,y|0鈮�x鈮�蟺4andsinx鈮�y鈮�cosx}

02

Step 2. Calculating the volume of the solid bounded above by the given function and region

The double integral is given by,

鈭�0蟺4鈭�sinxcosxf(x,y)dydx=鈭�0蟺4鈭�sinxcosxx2ydydx=鈭�0蟺4x2y22sinxcosxdx=鈭�0蟺4x2(cos2x-sin2x)2dx=鈭�0蟺4x2(cos2x)2dx

Integrating by parts, we get,

x2sin2x4+xcos2x4-sin2x80蟺4=蟺264+0-18-0+0-0=蟺2-864

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What is the difference between a double integral and an iterated integral?

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