Question

Integrate:-
\[ \int_0^{\frac \pi 2 } \sin^{2n} (x) dx \]

Answer 1

\[\large \int\limits_0^{\frac \pi 2 } \sin^{2n} (x) dx\]so it's readable ^_^

Answer 2

thanks @Jhannybean

Answer 3

This looks like a reduction formula.... \[\large \int\limits_{a}^{b}\sin^n(x)dx\cdots\]

Answer 4

yes, it looks like a reduction formula.

Answer 5

He states that reduction formula won't work here.

Answer 6

The indefinite integral is ulgy
http://www.wolframalpha.com/input/?i=integrate+sin%5E%282n%29x+

according to mathematica the integral evaluates to
\[ \int_0^{\frac \pi 2 } \sin^{2n} (x) dx = \frac{\sqrt \pi \Gamma(n + \frac 1 2)}{\Gamma (n +1)} \]

Answer 7

Woops!! looks like I got this one
http://math.stackexchange.com/questions/341402/int-0-pi-2-sin-x1-sqrt2-dx-and-int-0-pi-2-sin-x-sqrt2

Answer 8

should have realized
\[ \sqrt \pi = \Gamma (1/2)\]

Answer 9

Lol really? xD explain!!