`int_(0)^(pi//2)sin^(3)x dx=`

int_(0)^(pi/4) sin^(3) x dx=(2)/(3)

Evaluate the following : int_(0)^(pi)x sin^(3)x dx

int_(0)^(pi//2) sin ^(3) x cos^(3) x" "dx =

int_(0)^(pi//2)sin^(3)x cos^(4)x dx=

Evaluate : int_(0)^(pi//2) sin^(3) c cos x dx

int_(0)^(pi//2) sin ^(2) x cos^(3) x" "dx =

show that (a) int_(0) ^(2pi) sin ^(3) x dx = 0 , (b) int_(-1)^(1) e^(-x^(2)) dx = 2 int_(0)^(1) e^(-x^(2)) dx

int_(0)^(pi//2)sin^(4)x cos^(3)x dx =

int_(0)^(pi//2)(sin^(3//2)x)/((sin^(3//2)x+cos^(3//2)x))dx=(pi)/(4)