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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Evaluate the iterated integral.

4. 0 1 y 2 y 0 x + y 6 x y d z d x d y

To determine

To evaluate: The iterated integral.

Explanation

Given:

The function is f(x,y,z)=6xy .

The region is B={(x,y,z)|yx2y,0y2,0z(x+y)} .

Calculation:

The given integral is, 01y2y0x+y6xydzdxdy .

Integrate the given integral with respect to z and apply the limit.

01y2y0x+y6xydzdxdy=01y2y6xy[z]0x+ydxdy=01y2y6xy[(x+y)0]dxdy=01y2y6xy(x+y)dxdy=01y2y[6x2y+6xy2]dxdy

Integrate the given integral with respect to x and apply the limit.

01y2y0x+y6xydzdxdy=01[6yx33+6y2x22]y2ydy=01[(6y(2y)33+6y2(2y)22)(6

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Chapter 15 Solutions

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