Question

Steps for integrating

Answer 1

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

Answer 2

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

Answer 3

Yes

Answer 4

integration by parts twice

Answer 5

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"

Answer 6

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

Answer 7

Ah, thanks. I get it.

Answer 8

yw

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

using integration by parts ends up with that formula for reduction