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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 of the solid region hounded in the first octant by the plane

z = 4 2 x y .

To determine

To calculate: The volume of the solid region bounded in the first octane by the plane z=42xy.

Explanation

Given Information:

The provided plane is z=42xy.

Formula used:

The power of x formula of integration is xndx=xn+1n+1+C, where n1.

Calculation:

Consider the function,

z=42xy

The figure which shows the solid region of the plane z=42xy is given below,

The graph of the solid plane z=42xy in x-y plane is,

As it is clear that, the region R is bounded by the lines x=0,y=0,y=42x

From the graph of z=42xy in x-y plane, the limits of x is 0x2 which is outer limits.

The inner limit is 0y42x.

The volume of the region is,

02042x(42xy)dydx=02[4y2xyy22

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