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Chapter 13: Q. 32 (page 1015)

In Exercises 29鈥34, sketch the region determined by the limits of the iterated integrals and then give another iterated integral (or a sum of iterated integrals if necessary) using the opposite order of integration

鈭08鈭0y3f(x,y)dxdy

Short Answer

Expert verified

The sketch of the region is:

The iterated integral:

鈭02鈭x38f(x,y)dydx

Step by step solution

01

Step 1. Given information

Integral:

鈭08鈭0y3f(x,y)dxdy

02

Step 2. Sketch the region

The region is:

0鈮x鈮y30鈮y鈮8

The sketch of the region is:

03

Step 3. Change order of integral.

When x=0then y=0

When x=y3then y=x3

So by observing the above sketch we can change the order of integral as:

鈭02鈭x38f(x,y)dydx

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