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

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Homework Help Overview

The problem involves evaluating a double integral in polar coordinates to find the area in the first quadrant that lies below the line y=7 and between two circles defined by the equations x² + y² = 196 and x² - 14x + y² = 0.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the integral, with one attempting to integrate from specific bounds but questioning the correctness of the r values used. Others suggest the need for a visual representation of the region and consider breaking the problem into parts. There is also confusion regarding the polar equations corresponding to the curves involved.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the setup of the polar coordinates. Some guidance has been offered regarding the need to consider multiple curves and the implications of their polar representations.

Contextual Notes

There is mention of a professor providing partial guidance, but participants express uncertainty about the polar equations and the integration limits. The complexity of the region to be integrated is acknowledged.

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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
 
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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.
 
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
 
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?
 

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