Question 27

Mathematics Definite Integrals Hard

If \( I_n = \int_0^a (a^2 - x^2)^n \, dx \) where \( n \) is a positive integer, then the relation between \( I_n \) and \( I_{n-1} \) is:

(A) <span class="math-tex">\(\rm I_n = \left(\dfrac{2na^2}{2n+1}\right)I_{n-1}\)</span>
(B) <span class="math-tex">\(\rm I_n = \left(\dfrac{2n^2a^2}{2n+1}\right)I_{n-1}\)</span>
(C) <span class="math-tex">\(\rm I_n = \left(\dfrac{2na^2}{2n-1}\right)I_{n-1}\)</span>
(D) <span class="math-tex">\(\rm I_n = \left(\dfrac{2n^2a^2}{2n-1}\right)I_{n-1}\)</span>
View Dynamic Solution & Explanation
Correct Solution: Option A

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