`F(x)=int_2^(e^x)cost dt ,f i n dF^(prime)(x)`

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to a) -cosx (b) -sinx c) int_0^x(x-t)f(t)dt (d) 0

If F(x)= int_x^(x^2)e^(-t^4) dt then find F^1(x) .

If f(x) = int_(0)^(x^(2)) sqrt(cost)dt , find f'(x)

If f(x) = int_(0)^(x^(2)) sqrt(cost)dt , find f'(x)

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=

L e tf:[1,oo)->Ra n df(x)=int_1^x(e^t)/t dt-e^xdotT h e n f(x) is an increasing function lim_(x->oo)f(x)->oo f^(prime)(x) has a maxima at x=e f(x) is a decreasing function

f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(prime)(3)=4. Then the value of [f(10)]^2 − [ϕ(10)]^2is _____

f^(prime)(x)=varphi^(prime)(x)=f(x) for all xdot Also, f(3)=5a n df^(prime)(3)=4. Then the value of [f(10)]^2 - [ varphi(10)]^2 is _____

If f(x)=|x a a a x a a a x|=0, then f^(prime)(x)=0a n df^(x)=0 has common root f^(x)=0a n df^(prime)(x)=0 has common root sum of roots of f(x)=0 is -3a none of these

If f(x)=int_(x^2)^(x^2+1)e^(-t^2)dt , then f(x) increases in