Investigate for the maxima and minima of the function `f(x)=int_1^x[2(t-1)(t-2)^3+3(t-1)^2(t-2)^2]dt`

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Find the derivative of the function g(t) = ((t-2)/(2t+1)) .

Integrate the functions e^(t)((1)/(t)-(1)/(t^(2)))

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

Let f(x)=int_(2)^(x)f(t^(2)-3t+4)dt . Then

Consider the unction f(x)=int_(0)^(x)(5ln(1+t^(2))-10t tan^(-1)t+16sint)dt f(x) is

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) is

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

A function f(x) satisfies f(x)=sinx+int_0^xf^(prime)(t)(2sint-sin^2t)dt is

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2