`int_0^9[sqrt(t)]dt`

The function f(x)= int_0^x sqrt(1-t^4)dt is such that:

int sqrt(t)dt

int(1)/(sqrt(t))dt

For x in 0,(5pi/(2)), define f(x) = int_0^x sqrt(t) sin t dt . Then f has :

If f(x)=int_0^x (sint)/(t)dt,xgt0, then

I=int sqrt(1-t^(2))dt

The value of int_(0)^(sin^(2)) sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t)dt , is

The value of int_(0)^(sin^(2)x)sin^(-1)sqrt(t)dt+int_(0)^(cos^(2)x)cos^(-1)sqrt(t)dt is

Evaluate the following integrals using properties of integration : int_(0)^(sin^(2)x) sin^(-1) sqrt(t) dt + int_(0)^(cos^(2)x)sqrt(t) dt

The value of int _0^(sin^2x)sin^(-1)sqrt(t)dt+int _0^(cos^2x)cos^(-1)sqrt(t)dt is