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So, \(a^2 + 144 = 225\) → \(a^2 = 81\) → \(a = 9\).
Evaluate the integral \(\int_0^1 (3x^2 + 2x) \, dx\).
Integrate term by term: \(\int 3x^2 dx = x^3\), \(\int 2x dx = x^2\), so \(\int_0^1 (3x^2 + 2x) dx = [x^3 + x^2]_0^1 = (1 + 1) - (0 + 0) = 2\).

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