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Evaluate: int0^a(x^4)/(sqrt(a^2-x^2))dx...

Evaluate: `int_0^a(x^4)/(sqrt(a^2-x^2))dx`

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To evaluate the integral \( I = \int_0^a \frac{x^4}{\sqrt{a^2 - x^2}} \, dx \), we will use trigonometric substitution. ### Step 1: Trigonometric Substitution Let \( x = a \sin \theta \). Then, the differential \( dx \) becomes: \[ dx = a \cos \theta \, d\theta \] Also, we need to change the limits of integration: ...
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