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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

Calculate the double integral.

30. R tan θ 1 t 2 d A , R = { ( θ , t ) | 0 θ π / 3 , 0 t 1 2 }

To determine

To calculate: The value of given double integral over the region R.

Explanation

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy

Given

The rectangular region is, R={(x,y)|0θπ3,0t12} .

Calculation:

Compute the given double integral by using the formula stated above.

Rtanθ1t2dA=0π3[012tanθ1t2dt]dθ=01211t2dt

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Chapter 15 Solutions

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