y / | | /pi*x\ | sin|----| dx | \2*y / | / 2 y
Integral(sin((pi*x)/((2*y))), (x, y^2, y))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of sine is negative cosine:
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ /pi*x\ | 2*y*cos|----| | /pi*x\ \2*y / | sin|----| dx = C - ------------- | \2*y / pi | /
/ /pi*y\ |2*y*cos|----| | \ 2 / <------------- for And(y > -oo, y < oo, y != 0) | pi | \ 0 otherwise
=
/ /pi*y\ |2*y*cos|----| | \ 2 / <------------- for And(y > -oo, y < oo, y != 0) | pi | \ 0 otherwise
Piecewise((2*y*cos(pi*y/2)/pi, (y > -oo)∧(y < oo)∧(Ne(y, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.