2. Prove that, `int_(a)^(b) f(a+b-x) dx`= `int_(a)^(b) f(x) dx`

int_(a)^(b) x dx

int_(a)^(b) sin x dx

int_(a)^(b)cos x dx

int_(0)^(a)f(x)dx

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)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

If f(x)=f(a+b-x) for all x in[a,b] and int_(a)^(b) xf(x) dx=k int_(a)^(b) f(x) dx , then the value of k, is

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

Statement I The value of the integral int_(pi//6)^(pi//3) (dx)/(1+sqrt(tan x)) is pi/6 Statement II 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)/2int_a^bf(x)dx