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int(-pi)^(pi)x^(12)sin^(9)xdx=0...

`int_(-pi)^(pi)x^(12)sin^(9)xdx=0`

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To solve the integral \( I = \int_{-\pi}^{\pi} x^{12} \sin^9 x \, dx \) and show that it equals 0, we can follow these steps: ### Step 1: Define the Function Let \( f(x) = x^{12} \sin^9 x \). ### Step 2: Check the Symmetry of the Function To determine if the function is odd or even, we compute \( f(-x) \): \[ ...
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