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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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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 0101+x(3x+2y)dydx.

Formula used: Use the integration formula

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:

0101+x(3x+2y)dydx=01[3xy+2y22]01+xdx=01[(3x(1+x)+(1+x)2)(3x0+0)]dx=01

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Chapter 14 Solutions

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