`Let F`(x)= ` int_x 2t(5-t)``dt` .If `M` is the maximum value , of `F(x)` then the sum of the digits of `M` is

The maximum value of f(x) =int_(0)^(1) t sin (x+pi t)dt is

If f(x)=int_0^x tf(t)dt+2, then

Let f(x) = int_(0)^(x)|2t-3|dt , then f is

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

f(x)=int_0^x f(t) dt=x+int_x^1 tf(t)dt, then the value of f(1) is

Consider a real valued continuous function f such that f(x)=sinx + int_(-pi//2)^(pi//2) (sinx+t(f(t))dt . If M and m are maximum and minimum values of function f , then the value of M//m is____________.

Let f(x)=int_2^x(dt)/(sqrt(1+t^4))a n dg(x) be the inverse of f(x) . Then the value of g'(0)

Let f(x)=int_2^x (dt)/sqrt(1+t^4) and g be the inverse of f . Then, the value of g'(0) is

Let f(x) = int_(-2)^(x)|t + 1|dt , then

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)