int(sin^(-1)x)^(2)ul(t)

Let g(x) be differentiable on R and int_( sin t)^(1)x^(2)g(x)dx=(1-sin t), where t in(0,(pi)/(2)). Then the value of g((1)/(sqrt(2))) is

Antiderivative of int(sin^(2)x)/(1+sin^(2)x) w.r.t.x is

If int_(sin x)^(1) t^2 f(t) dt = 1 - sin x , then the value of f(1/(sqrt3)) is :

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is

For x epsilonR , and a continuous function f let I_(1)=int_(sin^(2)t)^(1+cos^(2)t)xf{x(2-x)}dx and I_(2)=int_(sin^(2)t)^(1+cos^(2)t)f{x(2-x)}dx . Then (I_(1))/(I_(2)) is

For x epsilonR , and a continuous function f let I_(1)=int_(sin^(2)t)^(1+cos^(2)t)xf{x(2-x)}dx and I_(2)=int_(sin^(2)t)^(1+cos^(2)t)f{x(2-x)}dx . Then (I_(1))/(I_(2)) is

For any x in R, and f be a continuous function Let I_(1) = int _(sin ^(2)x )^(1-cos ^(2)x) tf t (2-t)dt, I_(2) = int _(sin ^(2)x ) ^(1+cos ^(2)x) f (t(2-t))dt, then I_(1)=

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

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