Calculus

Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of quantity 2 times x to the 5th power plus 6 times x and 5 times x to the 4th power plus 3, dx. Your work must include the use of substitution and the antiderivative.

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  1. why, oh why, all those words? Ever hear of actual math notation? If I read it correctly, you want
    ∫[-1,0] (2x^5 + 6x)^3 * (5x^4 + 3) dx
    Note that if we let
    u = 2x^5 + 6x
    du = (10x^4+6) dx = 2(5x^4+3) dx
    That means that we just have
    ∫[-8,0] 1/2 u^3 du dx = 1/8 u^4 [-8,0] = -512

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    oobleck

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