Question

how can i integrate
∫x*(sin(x))^2

Answer 1

Intergration by parts

Answer 2

let x be u and sinx be dv

Answer 3

formula is uv-int(v.du)

Answer 4

Wait a second. I think the question is
\[ \int x \sin^2 x \ dx \] yes?

Answer 5

wouldnt assigning u to sin^2(x) be easier? it's a little confusing integrating sin^2(x)...im just suggesting i dunno which is easier in the end..jsyk

Answer 6

can you give me all serial solution

Answer 7

The first thing to is to get rid of the sin^2 term. Use a trig identity with cos(2x).

Answer 8

standard trick is to write
what jamesj said

Answer 9

cos(2x) = cos^2 x - sin^2 x
= 1 - 2.sin^2 x

Thus sin^2 x = ....

Answer 10

i couldnot solve it

Answer 11

\[ \sin^2 x = \frac{1}{2} (1 - \cos 2x) \]
Hence
\[ \int x . \sin^2 x \ dx = \frac{1}{2} \int (x - x.\cos 2x) \ dx \]
See what to do now?

Answer 12

go on

Answer 13

So you don't know what to do next? Surely you know how how to integrate the first part,
\[ \int x \ dx \] yes? Now, for the second part, use integration by parts.

Answer 14

thanks