prove that: `int_(0)^(1)x^2sin x dx >= (2/9)`

int_(0)^(pi) [2sin x]dx=

Prove that : int_(0)^(a) f(x) dx = int_(0)^(a) f(a-x)dx hence evaluate : int_(0)^(pi//2) (sin x)/(sin x + cos x) dx

prove that : int_(0)^(2a) f(x)dx = int_(0)^(a) f(x)dx + int_(0)^(a)f(2a-x)dx

int_(0)^(1) sin^(-1) x dx =(pi)/(2) -1

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

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

int_(0)^(pi//2)(1)/(2-sin x)dx=

Prove the equality int_(0)^(pi) f (sin x) dx = 2 int_(0)^(pi//2) f (sin x) dx

Prove that : int_(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii) Prove that " : int_(0)^(pi//2) sin 2x. log (tan-x) dx=0

Prove that int_(0)^(a) f(x) dx= int_(0)^(a) f(a-x)dx . Hence find int_(0)^((pi)/(2)) sin^(2) xdx