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Chapter 14, Problem 3RE
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### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

#### Solutions

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Section
BuyFindarrow_forward

### 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 1 ∫ 0 1 + x ( 3 x + 2 y ) d y   d x

To determine

To calculate: The value of the integral given as 0101+x(3x+2y)dydx.

Explanation

Given: The provided integral is âˆ«01âˆ«01+x(3x+2y)dydx.

Formula used: Use the integration formula

âˆ«xdx=x22

Use the identity

(a+b)2=a2+b2+2ab

Calculation: The function is firstly integrated with respect to y while 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«01âˆ«01+x(3x+2y)dydx=âˆ«01[3xy+2y22]01+xdx=âˆ«01[(3x(1+x)+(1+x)2)âˆ’(3xâ‹…0+0)]dx=âˆ«01

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