wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Choose the correct answer.
If f(x)=0x t sin t dt, then f'(x)is
(a)cos x+x sin x
(b)x sin x
(c)x cos x
(d)sin x +x cos x

Open in App
Solution

Given, f(x)=x0tsintdt
On integrating by parts, we get
f(x)=tx0sintdtx0[(ddtt)sintdt]dt=[t(cost)]x0x0(cost)dt=[tcost+sint]x0f(x)=xcosx+sinx
Now, differentiate w.r.t x,we get
f'(x)=-[{x(-sin x)}+cos x]+cos x=x sin x-cos x +cos x =x sin x
Using the product rule ddx(u.v)=udvdx+vdudx
Hence, option (b) is the correct answer.


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