# Area of a Polar Function

1. May 14, 2010

### Bryon

My question here is do I have the correct limits of integration? At first I thought it would be from pi/10 to 3pi/10 but I have a feeling that those are incorrect.

1. The problem statement, all variables and given/known data

Find the area of one petal of the polar function r(x) = cos(5x)

2. Relevant equations

integral[alpa to beta] .5* r(x)^2dx

3. The attempt at a solution

cos(5x) = 0 when x = (1/5)*pi/2 = pi/10
This means that the limits of integration are pi/10 and -pi/10

integral (.5*cos(5x))dx = 1/4x - (sin(5x)/20) from pi/10 to -pi/10

2. May 14, 2010

### Staff: Mentor

Yes, these are correct.
You have it in your relevant equations, but you forgot to square r(x) in the integral just above. Or maybe you just forgot to put in the exponent in your integrand.

3. May 14, 2010

### Bryon

Oops....sorry cos(5x)^2 = (1+cos(5x))/2

Thanks! for some reason I was thinking it was between pi/10 and 3pi/10.

4. May 14, 2010

### Mindscrape

That would work too. :)