If `f(x)` is differentiable and `int_0^(t^2)xf(x)dx=2/5t^5,` then `f(4/(25))` equals (a)`2/5` (b) `-5/2` (c)`1` (d) `5/2`

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

Evaluate int_(0)^(2)(5x)/((4+x^(2)))dx

Differentiate y = 4 cos(6x^2 + 5) .

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+x y)dx""=x""dy , then f(-1/2) is equal to: (1) -2/5 (2) -4/5 (3) 2/5 (4) 4/5

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

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

Differentiate the following : y=(x^(2)+4x+6 )^(5)

IfI_n=int_0^pie^x(sin"x")^("n")dx ,t h e n(I_3)/(I_1)"is equal to" 3/5 (b) 1/5 (c) 1 (d) 2/5

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

Differentiate y = (x^(3/4) sqrt(x^2 + 1))/((3x+2)^5) .