## anonymous one year ago Help with a few calc II problems for Trigometric Substitution? 10 | (100-x^2)^(1/2) dx 5 I have 6 others I am struggling with but I figured start one at a time. Thanks in advance.

1. anonymous

$\int\limits_{5}^{10} \sqrt{100-x^2}dx$ for a better version of the problem

Make the substitution of $$\sin \theta = \frac {x}{10}$$ $$10\cos \theta d\theta = dx$$ $\int \limits_5^{10} 10\sqrt{1-(x/10)^2}dx = \int \limits_{0.5}^{1} 10\sqrt{1-\sin^2\theta}(10\cos \theta )d\theta$

3. anonymous

That much I got.

tell us where is the problem then?

5. anonymous

Well, I don't know where to go from here. I've been struggling with trigometric problems since day 1 and this is so far the most obnoxiously difficult. Also I converted b and a into radians.

$100\cos \theta\sqrt{1-\sin^2\theta}= 100\cos^2 \theta$ The integral is finally sum up to- $100\int\limits_{0.5}^{1}\cos^2\theta d\theta$ use double angle identity to replace $$\cos ^2\theta$$ to $$\cos (2\theta)$$

7. anonymous

Ok. so $100\int\limits_{.5}^{1}\cos2 \theta d \theta.$ And from there? I'm really sorry, I have no idea what I'm doing with these. I just know the answer is supposed to be 25(2pi/3 - sqrt3/2)