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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Find the volume bounded by the surface

f ( x , y ) = e x 2 and the planes z = 0 , y = 0 , y = 2 x  and  x =1

To determine

To calculate: The volume bounded by the surface f(x,y)=ex2 and the planes z=0,y=0,y=2x and x=1.

Explanation

Given Information:

The provided function is f(x,y)=ex2 and the planes are z=0,y=0,y=2x and x=1.

Formula used:

The formula for integration by parts is udv=uvvdu.

The exponential rule of integral is exdx=ex+C.

Calculation:

Consider the function,

f(x,y)=ex2

In x-y planes, the region R are bounded by the lines y=0,x=1 and y=2x.

The region R is shown below,

Now double integrate the function by setting order of integration dydx.

V=0102xex2dydx=012xex2dx

First solve indefinite integral

V=2xex2dx …… (1)

Use integration by parts

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