Match the following
if
Column- I | Column- II |
(i) f(x) = | [A] + C |
(ii) f(x) = | [B] sin–1 + C |
(iii) f(x) = | [C] – 2 + cos–1 + + C |
(iv) f(x) = | [D] –tan–1 + C |
Text Solution
Verified by Experts(i) [D]; (ii) [B]; (iii) [A]; (iv) [C]
Ans.
(i) [D]
(ii) [B]
(iii) [A]
(iv) [C]
Sol. (i) Putting x = 1/t, I = 
, where f(x) is as in
we have I =
= 
= – 
(z 2 = 1 + 2t 2 )
= – 
= – tan –1 z = – tan –1 
+ C
(ii) Putting x + 2 = 1/t in I = 
where f(x) is as in We have I = 
= – 
= – sin –1 
= sin –1 
+ C
For (iii) As (1 –x 4 ) 7/2 = x 7 (1/x 2 – x 2 ) 7/2 , we can write
I = 
dx
Put x –2 –x 2 = t 2 , so that – 2(x –3 + x) dx = 2t dt
and I = – 
= 
+ C
= 
+ C
For (iv) Put 
= cos θ , i.e. x = cos 2 θ , so that
dx = – 2 cos θ sin θ d θ . Then
I = 
dx = 
(– sin 2 θ ) d θ
= – 
= – 4 
= – 2 
= – 2 
+ 
= –2 sin θ + θ + sin θ cos θ + C
= – 2 
+ cos –1 
+ 
+ C
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems