# Double integral to find the area of the region enclosed by the curve

1. Apr 10, 2005

### PhysicsMajor

Greetings all,

I need help setting up this problem:

Use a double integral to find the area of the region enclosed by the curve

r=4+3 cos (theta)

Thanks

2. Apr 10, 2005

### estalniath

Hello.

1)You'll have to draw a polar curve to help you out with this question. From the drawn polar curve, you'll get the minimum value of r to be 1. (when cos(theta) is negative)
2) Thus it follows that the range for r is 1<=r<=4+3cos(theta)
Hence we'll integrate r from 1 to 4+3cos(theta)
3) For the range of theta, you can use the range from 0 to pi for simplicity in calculations.(Just multiply the answer by 2 to obtain the full area.)

I hope this helps =)

3. Apr 10, 2005

### dextercioby

Yeah,a plot might help u convince why the limit wrt $\theta$ need to be 0 and $\pi$ and why you shouldn't integrate from 0 to $2\pi$

I think it's a cardioide.

Daniel.

Last edited: Apr 10, 2005