If `int_(0)^(t^(2)) x f(x) dx=(2)/(5) t^(5) , t gt 0`, then the value of `f((4)/(25))` is -

Let f (x) be differentiable and int _(0) ^(t^2) x f (x) dx = (1)/(2) t ^(4) for all t. Then the value of f (17) is

If f(x) is differentiable and int_(0)^(t^2)xf(x)dx=(2)/(5)t^5 ,then 5 f((4)/(25)) is equal to ....

If k int _(0)^(1)x.f(3x)dx = int_(0)^(3) t. f(t)dt , then the value of k is

If int_(0)^(x) f(t)dt=x+int_(x)^(1) t f(t) dt , then the value of f(1), is

If f(x) is differentiable and int_(0)^(t^(2))xf(x)dx=(2)/(5)t^(5) , then f((4)/(25)) equals

If f(x) is differentiable and int_(0)^(t^(2))xf(x)dx=(2)/(5)t^(5), then f((4)/(25)) equals (a)(2)/(5)(b)-(5)/(2)(c)1(d)(5)/(2)

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then the value of (23)/(2)f(0) is equal to

f(x)=int_(0)^( pi)f(t)dt=x+int_(x)^(1)tf(t)dt, then the value of f(1) is (1)/(2)