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Chapter 5: Q7P (page 247)

Question: In Problems 7 to 18 evaluate the double integrals over the areas described. To find the limits, sketch the area and compare Figures 2.5 to 2.7.

鈭�鈭�A(2x-3y)dxdywhere A is the triangle with vertices (0,0),(2,1),(2,0)

Short Answer

Expert verified

The required solution is 53.

Step by step solution

01

Definition of Double Integral

The outer bounds of a double integral must be constant, but the inner limits can be dependent on the outer variable.

02

Sketch the Integral

The lighter-colored area below is the integration area:

03

Finding the Integral

Consider the given integral and simplify,

鈭�鈭�A(2x-3y)dxdy=鈭�x=02鈭�y=0x/2(2x-3y)dydx=鈭�02(2xy-32y2)0x/2dx=鈭�02x2-38x2dx=鈭�0258x2dx=524x302=5脳824=53

Therefore, the solution is 53.

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