`int_(0)^(1)(cos^(-1)x)^(2) dx`

int_0^1(cos^(- 1)x)^2dx

Evaluate : int_(0)^(1) cos^(-1) dx

The value of int_(0)^(1)cos^(-1)((x-x^(2))-sqrt((1-x^(2))(2x-x^(2))))dx is equal to ___________.

Evaluate the following integral: int_0^1(cos^(-1)x)^2dx

If int_(0)^(1) cot^(-1)(1-x+x^(2))dx=k int_(0)^(1) tan^(-1)x dx , then k=

The value of int_(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int_(-1)^(1) cos^(-1)[x^(2)-(1)/(2)]dx , where [.] denotes the greatest integer function , is

Prove that for ngt1 . int_0^1(cos^-1x)^ndx=n(pi/2)^(n-1)-n(n-1)int_0^1(cos^-1x)^(n-2)dx

int_(0)^(1) (1)/(x^(2)+x+1)dx

Evaluate : (i) int_(0)^(1)(3sqrt(x^(2))-4sqrt(x))/(sqrt(x))dx , (ii) int_(0)^(1)x cos(tan^(1)x)dx

If agt0 and A=int_(0)^(a)cos^(-1)xdx, and int_(-a)^(a)(cos^(-1)x-sin^(-1)sqrt(1-x^(2)))dx=pia-lamdaA . Then lamda is