Question

Beta function
Please help!!!

Answer 1

\[\rm \int\limits_{0}^{2\pi} (1+cosx)^4~\cdot~\sin^2x~dx\]

Answer 2

@rishavraj @ganeshie8 @robtobey

Answer 3

@Michele_Laino

Answer 4

If I apply the bisection formulas, I can rewrite the integral as below:
\[\large I = 128\int_0^{2\pi } {{{\left\{ {\cos \left( {\frac{x}{2}} \right)} \right\}}^{10}}} {\left\{ {\sin \left( {\frac{x}{2}} \right)} \right\}^2}d\left( {\frac{x}{2}} \right)\]

Answer 5

i did not understand

Answer 6

Makes no sense to me either ¯\_(ツ)_/¯

Answer 7

@Zarkon please help

Answer 8

@zepdrix @Loser66 @mathmale @FibonacciChick666 @satellite73

Answer 9

hmmm

Answer 10

there is a way to do, but it takes a lot of time. hehehe. and I am lazy.
ok, expand the binomial, distribute sin^2 in, then take integral term by term

Answer 11

I meant (1+cos)^4= cos^4+4cos^3+6cos^2+4cos +1
then multiply sin^2 to each of them
then take integral term by term.

Answer 12

is it the only way?

Answer 13

i got another way!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
@Loser66 :)

Answer 14

anyways thank you !