If `(x)=int_0^x tsint\ dt ,\ ` then write the value of `f^(prime)(x)`

If f(x)=int_0^x(sint)/t dt ,x >0, then

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

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

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

If f(x)=-int_(0)^(x) log (cos t) dt, then the value of f(x)-2f((pi)/(4)+(x)/(2))+2f((pi)/(4)-(x)/(2)) is equal to

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

If xint_0^xsin(f(t))dt=(x+2)int_0^x tsin(f(t))dt ,w h e r ex >0, then show that f^(prime)(x)cotf(x)+3/(1+x)=0.

If f(x) attains a local minimum at x=c , then write the values of f^(prime)(c) and f^(prime)prime(c) .

If int_0^a3x^2dx=8,\ write the value of ' a^(prime)dot

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.