Double Integration in Polar Coordinates: Area Between Circles and Line y=7

[iamwilson]

Homework Statement

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=7,and between the circles x^2 + y^2 = 196 and x^2 - 14x + y^2 = 0.

Homework Equations

The Attempt at a Solution

i tried to double integrate from 0<theta<pi/2, 7-14cos(theta)<r<7 with rdrd(theta) but that was not the correct answe, can someone tell me with i did wrong with the r values

 

[Dick]

Did you draw a picture of the region you are integrating? If I'm drawing it correctly it doesn't look like you can do it as a single integral. You'll need to break it into pieces and think about using different origins for the polar coordinates for different pieces. Looks kind of nasty.

 

[iamwilson]

yes， i did, even ask my professor on how to doing it, but she only gave me the r=7+7cos(theta) but that doesn't make sense, i thought it's 14cos(theta), Dick, i completely loss, can anyone help me on this one

 

[Dick]

First of all there are three curves to worry about. The circle of radius 14, the circle of radius 7 and the line y=7. Which one corresponds to the polar equation r=7+7cos(theta)? What are the polar equations of the other two?