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Given \displaystyle \int_0^{\frac{3\pi}{2}} x^2\cos x \, dx = a - \frac{b\pi^2}{c}, where a, b and c are positive integers and b and c are coprime, what is the value of a + b + c?

  • Calulus -

    Man, can you cut the TEX?
    I think you have

    ∫[0,3π/2] x^2 cosx dx = a - bπ^2/c
    well, that's 2 - 9/4 π^2, so
    (a,b,c) = (2,9,4), so a+b+c=15

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