Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If I n = 
x n 
dx, prove that (n + 2) I n = –x n–1 (a 2 –x 2 ) 3/2 + (n –1) a 2 I n–2
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. We have,
I n = 
x n 
dx
⇒ I n = 
x n–1 
x dx
⇒ I n = – 
x n–1 
(–2x) dx
⇒ I n = – 
⇒ I n = – 
⇒ I n = – 
⇒ I n = – 
– 
⇒ I n = – 
x n–1 (a 2 –x 2 ) 3/2 + 
I n–2 – 
I n
⇒ I n 
= – 
x n–1 (a 2 –x 2 ) 3/2 + 
I n–2
⇒ (n +2) I n = –x n–1 (a 2 –x 2 ) 3/2 + (n –1)a 2 I n–2
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