find the area inside the cardiod r = 1 + cos(theta)

Limits, differentiation, related rates, integration, trig integrals, etc.
stellar
Posts: 22
Joined: Wed Mar 25, 2009 7:40 pm

find the area inside the cardiod r = 1 + cos(theta)

Postby stellar » Wed Aug 05, 2009 2:17 pm

find the area inside the cardiod r = 1 + cos(theta)

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stapel_eliz
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Postby stapel_eliz » Wed Aug 05, 2009 4:49 pm

For a lesson on how, in general, to find area with polar coordinates, try here. :wink:

From the graph, you know that the limits for this curve will be 0 and . The integral will then be:

. . . . .

By symmetry, this can be simplified a bit to:

. . . . .

. . . . .

By applying some trig identities, you should be able to get:

. . . . .

Then apply the standard trig-integral identity:

. . . . .

Integrate, evaluate, and you should be done! :D

stellar
Posts: 22
Joined: Wed Mar 25, 2009 7:40 pm

Re: find the area inside the cardiod r = 1 + cos(theta)

Postby stellar » Wed Aug 05, 2009 8:43 pm

thanks i got it! :mrgreen:


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