Chapter 14, Problem 4RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Evaluating an Integral In Exercises 3 - 6, evaluate the integral. ∫ 0 2 ∫ x 2 2 x ( x 2 + 2 y ) d y   d x

To determine

To calculate: The value of the integral given as 02x22x(x2+2y)dydx.

Explanation

Given: The provided integral is âˆ«02âˆ«x22x(x2+2y)dydx.

Formula used: Use the integration formula;

âˆ«xdx=x22

Calculation: The function is firstly integrated with respect to y, taking x as a constant. Then, the limit of y is substituted. Again, the obtained function is integrated with respect to x.

The integral is solved as follows:

âˆ«02âˆ«x22x(x2+2y)dydx=âˆ«02[x2y+2y22]x22xdx=âˆ«02[(x2â‹…2x+(2x)2)âˆ’(x2â‹…x2+(x2)2)]dx<

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