The no.of positive real solutions of the equation `int_(0)^(x)(e^(t))/(1+t)dt=x+1` is

The number of integral solutions of the equation 4int _(0)^( infty)(In" t"dt)/(x^(2)+t^(2))-piIn 2 =0, x gt 0, is

no.of solutions of the equation e^(sin""x)- e^( -sin""x)-4""=""0

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

The total number for distinct x epsilon[0,1] for which int_(0)^(x)(t^(2))/(1+t^(4))dt=2x-1 is __________.

Find the equation of tangent to y=int_(x^2)^(x^3)(dt)/(sqrt(1+t^2))a tx=1.

If the solution of the equation (d^(2)x)/(dt^(2))+4(dx)/(dt)+3x = 0 given that for t = 0, x = 0 and (dx)/(dt) = 12 is in the form x = Ae^(-3t) + Be^(-t) , then

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

Find the value of ln(int_(0)^(1) e^(t^(2)+t)(2t^(2)+t+1)dt)

Let f be a differentiable function on R and satisfying the integral equation x int_(0)^(x)f(t)dt-int_(0)^(x)tf(x-t)dt=e^(x)-1 AA x in R . Then f(1) equals to ___

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=