Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Assuming that 
= – π log 2, show tha
= – 
.
Text Solution
Verified by ExpertsThe correct answer is:
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Sol. Let
I = 
... (i)
Then,
I = 
⇒ I = 
... (ii)
Adding (i) and (ii), we get
2I = 
⇒ 2I = 
⇒ 2I = π 3 
+3 π 
–3 π 2 
⇒ 2I = – π 4 log 2 – 3 π 2 
+3 π 
⇒ 2I = – π 4 log 2 –3 π 2 I 1 + 3 π I 2 ... (i)
where,
I 1 = 
and I 2 = 
Now,
I 1 = 
⇒ I 1 = 
⇒ I 1 = 
⇒ I 1 = 
– 
⇒ I 1 = π –I 1
⇒ 2I 1 = π 
⇒ 2I 1 = π (– π log 2)
⇒ I 1 = – 
log 2
Putting the value of I 1 in (i), we get
2I = – π 4 log 2 –3 π 2 × 
log 2 + 3 π I 2
⇒ 2I = 
log 2 + 3 π I 2
⇒ I = 
log 2 + 
I 2
⇒ 
= 
log 2 + 
= 
× 
log 2 + 
= 
× 
log 
+ 
= 
+ 
= 
= 
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