Prove that `int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx`

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx

Prove that int_(a)^(b) f(x) dx= int_(a)^(b) f(a+b-x) dx

If f(a+b-x)=f(x), then prove that int_(a)^(b)xf(x)dx=(a+b)/(2)int_(a)^(b)f(x)dx

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

int_(a)^(b)f(x)dx=phi(b)-phi(a)

Prove that int_(0)^(2a)f(x)dx=int_(a)^(a)[f(a-x)+f(a+x)]dx

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

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

int_(a)^( If )f(x)dx=((b-a)lambda)/(8)int_(0)^(1)f((b-a)x+a)dx

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