`int_(0)^(2pi)(sinx+cosx)dx=`

Evaluate :- int_(0)^(pi//2)(sinx+cosx)dx

Consider the definite integrals A=int_(0)^(pi)sinx cosx^(2)xdx and B=int_(0)^((pi)/(2))sinx cos^(2)xdx . Then,

The value of int_(-pi)^(pi) sinx f(cosx)dx is

int_(0)^(2pi)|sinx|dx=?

Evaluate int_(0)^(pi//2)|sinx-cosx|dx .

Evaluate: int_0^(pi//2)x/(sinx+cosx)dx

Evaluate int_0^(pi/2) x/(sinx+cosx)dx

int_(0)^(pi//2)((sinx-cosx))/((1+sinxcosx))dx=0

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

I_(1)=int_(0)^((pi)/2)(sinx-cosx)/(1+sinxcosx)dx, I_(2)=int_(0)^(2pi)cos^(6)dx , I_(3)=int_(-(pi)/2)^((pi)/2)sin^(3)xdx, I_(4)=int_(0)^(1) In (1/x-1)dx . Then