CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If f is strictly increasing and positive function, such that xx0(1t)sin(f(t))dt=2x0tsin(f(t))dt, where x>0. Then the value of f(x)cotf(x)+31+x in the domain of f(x) is

Open in App
Solution

Given expression is
xx0(1t)sin(f(t))dt=2x0tsin(f(t))dt
Differentiating w.r.t. x using Leibnitz theorem, we get
x0(1t)sin[f(t)]dt+x(1x)sin[f(x)]=2xsin[f(x)]
x0(1t)sin[f(t)]dt=xsin[f(x)](1+x)
Again differentiating w.r.t. x, we get
(1x)sin[f(x)]=(x+x2)cos[f(x)]f(x)+(2x+1)sin[f(x)]
3xsin[f(x)]=(x+x2)cos[f(x)]f(x)
3xx(1+x)=cot[f(x)]f(x)
f(x)cotf(x)+31+x=0

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
CHEMISTRY
Watch in App
Join BYJU'S Learning Program
CrossIcon