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Chapter 13: Q. 18 (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�蟺/23蟺/2鈭�14r3/2drd胃

Short Answer

Expert verified

鈭�蟺/23蟺/2鈭�14r3/2drd胃=625蟺

Step by step solution

01

Draw the region.

The region determined by the limits is shown below,

02

Evaluate the integral

I=鈭�蟺/23蟺/2鈭�14r3/2drd胃I=鈭�蟺/23蟺/2r32+132+114d胃I=25鈭�蟺/23蟺/2r5214d胃I=25鈭�蟺/23蟺/2452-152d胃I=2脳315鈭�蟺/23蟺/2d胃I=6253蟺2-蟺2I=625蟺

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Most popular questions from this chapter

Identify the quantities determined by the integral expressions in Exercises 19鈥�24. If x, y, and z are all measured in centimeters and 蚁(x, y,z) is a density function in grams per cubic centimeter on the three-dimensional region , give the units of the expression.

鈭�惟鈥�x2+z2蚁(x,y,z)dV

Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32

鈭�鈭�Rx2y3dAWhereR={(x,y)|1鈮�x鈮�3,0鈮�y鈮�2}

Find the masses of the solids described in Exercises 53鈥�56.

The first-octant solid bounded by the coordinate planes and the plane 3x + 4y + 6z = 12 if the density at each point is proportional to the distance of the point from the xz-plane.

Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.

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�Rx2ydAWhereR={(x,y)|-1鈮�x鈮�0,0鈮�y鈮�2}
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