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

If 10tan1xdx=α, then π/40tan1(2cos2θ2sin2θ)sec2θdθ is equal to

A
α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
α2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2α
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 2α
Given : 10tan1xdx=α
I=π40tan1[2cos2θ2(sin2θ)]sec2θdθI=π40tan1[22sec2θ2tanθ]sec2θdθI=π40tan1[1tan2θtanθ+1]sec2θdθLet:t=tanθθ0t0dt=sec2θdθθπ4t1I=10tan1[1(t2t+1)]dtI=10tan1[t(t1)1+t(t1)]dtI=10tan1tdt10tan1(t1)dtI=10tan1tdt10tan1(1t1)dtI=10tan1tdt+10tan1(t)dtI=210tan1tdt=2α
Hence the correct answer is 2α.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Property 1
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon