pi -- 2 / | | 12*y*sin(2*x*y) dy | / pi -- 4
Integral((12*y)*sin((2*x)*y), (y, pi/4, pi/2))
// 0 for x = 0\ || | / || //sin(2*x*y) \ | // 0 for x = 0\ | || ||---------- for 2*x != 0| | || | | 12*y*sin(2*x*y) dy = C - 12*|<-|< 2*x | | + 12*y*|<-cos(2*x*y) | | || || | | ||------------ otherwise| / || \\ y otherwise / | \\ 2*x / ||----------------------------- otherwise| \\ 2*x /
/ /pi*x\ /pi*x\ | 3*sin|----| 3*pi*cos|----| | \ 2 / 3*sin(pi*x) 3*pi*cos(pi*x) \ 2 / |- ----------- + ----------- - -------------- + -------------- for And(x > -oo, x < oo, x != 0) < 2 2 x 2*x | x x | | 0 otherwise \
=
/ /pi*x\ /pi*x\ | 3*sin|----| 3*pi*cos|----| | \ 2 / 3*sin(pi*x) 3*pi*cos(pi*x) \ 2 / |- ----------- + ----------- - -------------- + -------------- for And(x > -oo, x < oo, x != 0) < 2 2 x 2*x | x x | | 0 otherwise \
Piecewise((-3*sin(pi*x/2)/x^2 + 3*sin(pi*x)/x^2 - 3*pi*cos(pi*x)/x + 3*pi*cos(pi*x/2)/(2*x), (x > -oo)∧(x < oo)∧(Ne(x, 0))), (0, True))
Use the examples entering the upper and lower limits of integration.