Question

Need help with this integral

Answer 1

\[\int\limits_{0}^{a} \sin \left( \frac{ n \pi x}{ a } \right)\sin^3\left( \frac{ \pi x }{ a } \right)dx \] I used product sum identity and its not getting me anywhere useful

Answer 2

@ganeshie8

Answer 3

\[\dfrac{a}{\pi}\int\limits_{0}^{\pi} \sin \left( n x \right)\sin^3\left( x \right)dx\]

Answer 4

what do we know about \(n\) ?

Answer 5

is it an integer ?

Answer 6

Yup

Answer 7

It's a bit tricky to answer, as it has to do with coefficients for a wave function lol

Answer 8

I used \[\frac{ 1 }{ 2 }[\cos(u-v)-\cos(u+v)]\] but it doesn't seem right

Answer 9

Oh you know what I forgot about the cubed

Answer 10

Maybe first consider even values of \(n\)

Answer 11

Yeah I ended up with 0 for both odd and even

Answer 12

Which is not good! Ha!

Answer 13

You should get \(0\) when \(n\) is even
it cannot be \(0\) when \(n\) is odd

Answer 14

Ah ok, I'm going to redo it and see what I get

Answer 15

http://www.wolframalpha.com/input/?i=Table%5B%5Cint_0%5E(pi)+sin(n*x)sin%5E3(x),+%7Bn,1,10%7D+%5D

Answer 16

Wow that looks good!

Answer 17

I have look at the case when n is even
it is definitely 0

Answer 18

looks it is 0 for n > 3

Answer 19

Yeah I forgot it was sin^3(...) and was treating it like sinx and it made it funky

Answer 20

Thanks