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Chapter 13: Q. 19 (page 1082)

Using polar coordinates to evaluate iterated integrals: Sketch the region determined by the limits of the given iterated integrals, and then evaluate the integrals.

鈭�0蟺/2鈭�02sin胃r3drd胃

Short Answer

Expert verified

鈭�0蟺/2鈭�02sin胃r3drd胃=34蟺

Step by step solution

01

Draw the region

The region determined by the limits is shown below,

02

Evaluate the integral

I=鈭�0蟺/2鈭�02sin胃r3drd胃I=鈭�0蟺/2r4402sin胃d胃I=164鈭�0蟺/2sin4胃d胃I=4鈭�0蟺/2sin4胃d胃I=434路12路蟺2I=34蟺

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Most popular questions from this chapter

Explain why using an iterated integral to evaluate a double integral is often easier than using the definition of the double integral to evaluate the integral.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals

鈭�鈭�R(2-3x2+y3)dAWhereR={(x,y)|-3鈮�x鈮�2,3鈮�y鈮�5}

Howmanysummandsarein鈭�i=215鈭�j=317鈭�k=419ij+k?

Evaluate Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32

鈭�鈭�Rxy3dAWhereR={(x,y)|-2鈮�x鈮�2,-1鈮�y鈮�1}

In Exercises 61鈥�64, let R be the rectangular solid defined by R=(x,y,z)|0鈮�a1鈮�x鈮�a2,0鈮�b1鈮�y鈮�b2,0鈮�c2鈮�z鈮�c2.

Assume that the density of R is uniform throughout, and find the moment of inertia about the x-axis and the radius of gyration about the x-axis.
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