Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If I n = 
x n (a –x) 1/2 dx, prove that (2n + 3) I n = 2an I n–1 – 2x n (a –x) 3/2
Text Solution
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CHECK THE SOLUTION.
Sol. We have,
I n = 
⇒ I n = 
x n (a –x) 3/2 + 
x n–1 (a –x) 3/2 dx
⇒ I n = 
x n (a –x) 3/2 + 
x n–1 (a –x) (a –x) 1/2 dx
⇒ I n = – 
x n (a –x) 3/2 + 
x n–1 (a –x) 1/2 dx
– 
x n (a –x) 1/2 dx
⇒ I n = 
x n (a –x) 3/2 + 
I n–1 – 
I n
⇒ 
I n = 
x n (a –x) 3/2 + 
I n–1
⇒ (2n + 3) I n = –2x n (a –x) 3/2 + 2an I n–1
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