Question

Integrate sin(nx)sin(x) over [0, pi] - Wave Equation

Answer 1

multiply and divide the given expression by 2
then use the formula
2sin(A)sin(B) = cos(A - B ) - cos (A+B)

Answer 2

I end up with the answer \[1/2\left[ 1/(n+1)\sin (1+n)x - 1/(n-1)\sin (1-n)x \right]^{\pi}_{0}\] which according to me should be 0 for any value of n

Answer 3

what if n=1

Answer 4

\[\int\limits_{0}^{\pi}\sin(x)\sin(x)dx=\frac{\pi}{2}\]

so it is not 0 everywhere

Answer 5

@zarkon for n= 1 it is pi/2
for the rest value of n it is coming out to be zero

Answer 6

for positive integer n ...I know that