# Math Help - polar coordinates

1. ## polar coordinates

any one here good with finding area of surface of revolution or arc length in polar coordinate system?

2. I finally got one of the problems I was working on. Now stuck on find the length of the curve over the given interval.

r=8(1+cos theta) [0, 2pi]
r=8+8 cos theta
r`=-8 sin theta

Arc length= 2 $\int_0^\pi\sqrt{(8+8~cos\theta)^2+(-8~sin\theta)^2}~d\theta=2\int_0^\pi\sqrt{64+128~co s\theta+64~cos^2\theta+64~sin^2\theta}~d\theta$

I am stuck at this point.

3. $2 \int_{0}^{\pi} \sqrt{64 + 128 \cos \theta + 64 \cos^{2} \theta + 64 \sin^{2} \theta} \ d \theta = 2 \int_{0}^{\pi} \sqrt{128(1 + \cos \theta)} \ d \theta$ $= 2 \sqrt{128} \int_{0}^{\pi} \sqrt{1 + \cos \theta} \ d \theta = 4 \sqrt{128} \sqrt{\cos x +1} \tan \left(\frac{x}{2} \right)$.