Match each double integral in polar with the graph of the region of integration.

Question

Match each double integral in polar with the graph of the region of integration. 2 pi integrate 0 4 integrate 3 f(r,theta)r dr d heta 2pi integrate 3pi/2 4 integrate 0 f(r,theta)r dr d theta 3 integrate 0 3pi/4integrate 0 f(r,theta)r dtheta dr 4 integrate 3 7pi/4 integrate 3pi/4 f(r,theta)r dtheta dr 3pi/2 integrate 3pi/4 3 integrate 0 f(r,theta)r dr dtheta 3pi/4 integrate -pi/4 4 integrate -pi/2 f(r,theta)r dr dtheta 3 integrate 0 3pi/4 integrate -pi/2 f(r,theta)r dtheta dr 2pi integrate 0 3 integrate 0 f(r,theta)r dr dtheta

Explanation / Answer

1 -B as region is circular shell between circles of radius 3 and 4

2- D as region is part of the circle between theta = 3pi/2 and 2pi.

3-E as region is part of the circle between theta = 0 to 3pi/4

4-F as region is part of the circular shell between r =3 to 4 and theta = 3pi/4 to 7 pi/4

5-A as region is part of the circle between theta = 3pi/4 to 3pi/2

6-G as region is part of the circular shell between r =3 to 4 and theta = -pi/4 to 3pi/4 (i.e. in counterclockwise direction)

7 -C as region is part of the circle between theta = -pi/2 to 3pi/4 ( i.e. in counterclockwise direction)

8-H as region is full circle.

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