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March 25, 2017

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Evaluate the following definite integral:

integral at a = -1, b=2

-4dx/(9x^2+30x+25)

Would I have to separate them in 3 terms as:

-4 ∫1/9x^2 + ∫1/30x + ∫1/25

resulting in: -4/(3x^3)+ (15x^2)+ C?

and from there I can replace a and b

f(a) - f(b)?

Thank you

  • Calculus - ,

    Booo!

    1/(a+b+c) is NOT 1/a + 1/b + 1/c

    What you need to do is let

    u = 3x+5 and you have
    du = 3 dx, so dx = du/3
    x in [-1,2] means u in [2,11]
    giving you
    ∫[2,11] -4/u^2 du/3
    -4/3 ∫[2,11] u^-2 du

    That should be ever so simple.

  • Calculus - ,

    THanks Steve, but why 3x+5??

  • Calculus - ,

    because you have 9x^2 + 30x + 25 = (3x+5)^2

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