## anonymous 4 years ago Steps for integrating

1. anonymous

$\int\limits_{\pi/4}^{\pi/2} (2\sin \theta)^2 d \theta$

2. anonymous

i take it this is the same as $4\int \sin^2(x)dx$ right?

3. anonymous

Yes

4. dumbcow

integration by parts twice

5. anonymous

gimmick is to write $\sin^2(x)=1-\cos^2(x)=\frac{1}{2}-\frac{1}{2}\cos(2x)$ one of those "double angle formula's backwards"

6. anonymous

best trick is actually to look in the back of the textbook for the "reduction formulas" but if you recall all those annoying trig identities, this is the "lowering powers" formula

7. anonymous

Ah, thanks. I get it.

8. anonymous

yw

9. amistre64

sin reduction:$\int sin^ndx=-\frac{1}{n}sin^{n-1}cos+\frac{n-1}{n}\int sin^{n-2}dx$

10. anonymous

yeah that one that i can't remember. the entire content of most calc 2 courses is contained on the back two pages of the text

11. anonymous

I've never seen that formula but wouldn't that give me another answer?

12. amistre64

the answer might "look" different, but since trig has identities that are equal it will have the same value in the end

13. amistre64

using integration by parts ends up with that formula for reduction