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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 triple integral.

18. E z d V , where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant

To determine

To evaluate: The integral of EzdV .

Explanation

Given:

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

The region is E={(x,y,z)|0x1,3y3x,0z9y2} .

Calculation:

The given integral is, EzdV=013x309y2zdzdydx .

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

EzdV=013x3[z22]09y2dydx=12013x3[(9y2)20]dydx=12013x3[9y2]dydx

Integrate the given integral with respect to y and apply the limit of it

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Chapter 15 Solutions

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P-52RECh-15 P-53RECh-15 P-54RECh-15 P-55RECh-15 P-56RECh-15 P-57RECh-15 P-58RECh-15 P-59RECh-15 P-60RECh-15 P-1PCh-15 P-2PCh-15 P-3PCh-15 P-4PCh-15 P-5PCh-15 P-6PCh-15 P-7PCh-15 P-8PCh-15 P-9PCh-15 P-10PCh-15 P-11PCh-15 P-12PCh-15 P-13P

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