If `x int_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.`

Similar Questions

Explore conceptually related problems

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

If f(x)=int_0^x (sint)/(t)dt,xgt0, then

If f(x)=int_(0)^(x)tf(t)dt+2, then

If int_(0)^(1) f(t)dt=x^2+int_(0)^(1) t^2f(t)dt , then f'(1/2)is

If int_(0)^(x)f(t)dt=x+int_(x)^(1)f(t)dt ,then the value of f(1) is

If int_(0)^(x) f(t)dt=x^(2)+2x-int_(0)^(x) tf(t)dt, x in (0,oo) . Then, f(x) is

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is

If int_(0)^(x^(2)(1+x))f(t)dt = x then find f(2)