   Chapter 14.2, Problem 10E

Chapter
Section
Textbook Problem

Evaluating a Double IntegralIn Exercises 7–12, sketch the region R and evaluate the iterated integral ∫ R ∫ f ( x , y ) d A . ∫ 0 4 ∫ y / 2 y x 2 y 2 d x d y

To determine

To graph: The iterated integral 04y2yx2y2dxdy and sketch of the region R.

Explanation

Graph:

Calculate the region:

Here the limit of y is from 0 to 4 and that of x is from y2 to y.

As x=y2,

It is a straight line which passes through the origin and x=y is equation of parabola.

The intersection points of line is calculated as,

y2=yy24=yy24y=0y(y4)=0

On further calculation,

y=0,4.

Substitute the value of y in the relation of x.

Then,

x=y2=42=2

So, the intersection point is (0,0) and (2,4).

Formula used:

The integral of, xndx=xn+1n+1+c

Calculation:

The region R can be sketch with the following values:

The point y goes from 0 to 4 and x goes from y2 to y

Now, evaluat

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