Question

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.

Answer 1

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

Answer 2

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

Answer 3

That much I got.

Answer 4

tell us where is the problem then?

Answer 5

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.

Answer 6

\[100\cos \theta\sqrt{1-\sin^2\theta}= 100\cos^2 \theta\]

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 \(\cos (2\theta)\)

Answer 7

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)