Suppose that `F(x)` is an anti derivative of `f(x)=(sinx)/x`, where `xgt0`. Then `int_(1)^(3)(sin2x)/x dx` can be expressed as

Suppose that F (x) is an antiderivative of f (x)=sinx/x,x>0 , then int_1^3 (sin2x)/x dx can be expressed as

If the anti derivative of int sin^4x/x dx is f(x) then int(sin^4(p+q)x)/x dx in terms of f(x) is

Find the derivative for function f(x)=2sinx+sin2x with respect to x

Find the anti derivative F of f defined by f(x)=4x^3-6 , where F (0) = 3

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

If f(x) = int(2sinx-sin2x)/(x^(3)) dx, where xne0 , then Limit_(xto0) f^(')(x) has the value

If f(0)=2,f'(x)=f(x),phi(x)=x+f(x)" then "int_(0)^(1)f(x)phi(x)dx is

Let F : R to R be a thrice differentiable function . Suppose that F(1)=0,F(3)=-4 and F(x) lt 0 for all x in (1,3) . f(x) = x F(x) for all x inR . If int_(1)^(3)x^(2)F'(x)dx=-12 andint_(1)^(3)x^(3)F'' (x)dx =40 , then the correct expression (s) is //are

Prove that int_(0)^(oo) (sin^(2)x)/(x^(2))dx=int_(0)^(oo) (sinx)x dx