If I_n = x^n a^2 - x^2 dx

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

If In=∫xna2−x2dxI_n = \int x^n \sqrt{a^2 - x^2} dx, prove that In=−xn−1(a2−x2)3/2(n+2)+(n−1)(n+2)a2In−2.I_n = -\frac{x^{n-1} (a^2 - x^2)^{3/2}}{(n+2)} + \frac{(n-1)}{(n+2)} a^2 I_{n-2}.

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