Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Evaluate
(i) 
(ii) 
dx
(iii) 
dx, a > b (iv) 
dx
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(i) 
– n 2 (ii) 
(iii) – 
(b – a) 2 (iv) π 
– n 4
Sol. (i) Ι = 
Let x = tan θ ⇒ dx = sec 2 θ d θ
⇒ Ι = 
= 2 
= 
= 
= 
(ii) Let tan –1 x = t ⇒ 
= dt
∴ Ι = 
= 
= 
(iii) Ι = 
put x = a sin 2 θ + b cos 2 θ
Ι = 2 
; Ι = – 2 (b – a) 2 
Ι = – 
; Ι = – 
= – 
(iv) Ι = 
put x = tan θ ∈ 
, 2 θ ∈ 
Ι = 
= 
+ 
= 
– 
= 
– 
Ι = π 
– n 4. Ans.
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