Question

Not as easy at it looks. u = sin(x) doesn't work.\[\int {\sin^2 x dx}\]

Answer 1

use trig formulas \[\sin^2 x = \frac{1 - \cos (2x)}2\]

Answer 2

if i recall right, that is the formula for sin^2 x

Answer 3

\[\sin^2x = {1 - \cos ^2x}\]\[\implies{ {1 - {\cos(2x }) \over 2}}\]

Answer 4

Yeah, right.

Answer 5

so now integrate that

Answer 6

integration by parts and the reduction formulae would work as well!

Answer 7

@Omniscience can you explain?

Answer 8

i doubt IBP would work

Answer 9

It does!

Answer 10

hmm yeah it does

Answer 11

@lgbasallote I see what you did there, but let's see what Omni says :)

Answer 12

for the reduction formulae google it; im too lazy to derive it right now :P

Answer 13

Okay, well :)

Answer 14

"for integration by parts you can do that on your own" ~Omni

Answer 15

Ah yes, the famous "this part is left as an exercise for the reader." Also lazy, I just typed it into maxima and got

\[\frac{x-\frac{sin(2x)}{2}}{2}\]

Answer 16

I got my answer using lgb's method, but haha I couldn't get reduction formulae from Wikipedia!

Answer 17

http://www.intmath.com/methods-integration/10-integration-reduction-formulae.php

Answer 18

if i have time; i will derive it..if its not googeable

Answer 19

wolfram alpha is the math wikipedia

Answer 20

anyway; just use the trig method, easier

Answer 21

Ho! Ho! Ho! I found an appropriate method somewhere ;) by the way, it's the same as LGB's.

Answer 22

you learnt complex nos ? you can use that too here..