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Chapter 9: Q. 42 (page 756)

Polar coordinates to sketch the region and evaluate the expressions.

3鈭�0蟺2sin23胃d胃

Short Answer

Expert verified

The graph of the region is

The value of the integral is3蟺4.

Step by step solution

01

Step 1. Given Integral

The given integral is3鈭�0蟺/2sin2(3胃)d胃.

02

Step 2. Plot the Region

  • The general equation to find the area of a region is A=12鈭�伪尾(f(胃))2d胃, where f(胃)is the region.
  • On comparing the general equation to the given integral, the region is sin(3胃).
  • Use the graphing utility to plot the function.

03

Step 3. Integrate

Integrate the given integral as shown below:

3鈭�0蟺/2sin2(3胃)d胃=32鈭�0蟺/21-cos(6胃)d胃=32鈭�0蟺21d胃-鈭�0蟺2cos6胃d胃=32蟺2-0=3蟺4

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Most popular questions from this chapter

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

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Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

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Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

directrixx=3, focus(0,1)
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