Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If u n = 
dx, prove that
u n = – 
+ 
a 2 u n– 2
A
u n = – 
+ 
a 2 u n–2
+ a 2 u n–2
B
u n = 
+ 
a 2 u n–2
+ a 2 u n–2
C
u n = 
+ 
a 2 u n–2
+ a 2 u n–2
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
u n = 
dx = 
{x 
} dx
Integrating by parts taking x n–1 as first function, we have
= x n–1 
+
dx
⇒ u n = – 
+ 
(a 2 – x 2 ) 
dx
⇒ u n = – 
+ 
u n – 2 – 
u n
⇒ 
u n = – 
+ 
⇒ u n = – 
+ 
a 2 u n– 2
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