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March 26, 2017

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Evaluate the definite integral from 0 to 1 of

(x^2)sqrt(5x+6)dx

  • Calc 2 - ,

    ∫[0,1] x^2 √(5x+6) dx
    That's almost x^5/2, but for that pesky 5x+6. So, let u=5x+6 and we have x = (u-6)/5:

    ∫[6,11] (u-6)^2/25 √u du/5
    = 1/125 ∫[6,11] u^(5/2) - 12u^(3/2) + 36u^(1/2) du
    = 1/125 (2/7 u^7/2 - 24/5 u^5/2 + 24u^3/2)[6,11]
    = 2/4375 (576√6 - 1111√11)
    = 1.03948

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