`(d)/(dx)int_(x^(2))^(x)sqrt(cost)dt` (at `x=0`) equals to ________.

(d)/(dx)(int_(x^(2))^((x^(3)) (1)/(logt)dt) is equal to

If f(x) = int_(0)^(x^(2)) sqrt(cost)dt , find f'(x)

(d)/(dx)(int_(f(x))^(g(x)) phi(t)dt) is equal to

Evaluate (d)/(dx)(int_(1//x)^(sqrtx) cos t^(2) dt)

According to Leibritz differentiation under the sign of integration can be performed as as below. (i) (d)/(dx)[int_(phi(x))^(Psi(x))f(t)dt]=f{Psi(x)}xx(d)/(dx){Psi(x)}-f{phi(x)}xx(d)/(dx){phi(x)} (ii) (d)/(dx)[int_(phi(x))^(Psi(x))f(x,t)dt]=int_(phi(x))^(Psi(x))(del)/(delx)(f(x,t)dt)+f(x,Psi(x))xx(d)/(dx)Psi(x)-f(x,phi(x))xx(d)/(dx)(phi(x)) int_(x^(2))^(x^(3))cost^(2)dt has the derivative

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to : (a) 0 (b) 2e (c) 2e^2 -2 (d) e^2-e

lim_(x to 0)(int_(0)^(x^(2))(tan^(-1)t)dt)/(int_(0)^(x^(2))sin sqrt(t)dt) is equal to :

Let f(x) be a differentiable function symmetric about x=2 , then the value of int_(0)^(4)cos(pix)f'(x)dx is equal to________.

If int_(0)^(x)f(t)dt=x^2+int_(x)^(1)\ t^2\ f(t)dt , then f((1)/(2)) is equal to (a) (24)/(25) (b) (4)/(25) (c) (4)/(5) (d) (2)/(5)

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of int_(0)^(pi//2) f(x)dx lies in the interval