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Math Help - How do you solve this integral?

  1. #1
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    How do you solve this integral?

    ∫ (from 0 to 3) (((3x)^(1/2)+1) - (x+1)) dx

    Can you solve it showing your work please? My professor says it's 1.5, and I can't seem to come to that. Any help would be appreciated! Thanks!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Spika View Post
    ∫ (from 0 to 3) (((3x)^(1/2)+1) - (x+1)) dx

    Can you solve it showing your work please? My professor says it's 1.5, and I can't seem to come to that. Any help would be appreciated! Thanks!
    Is this what you mean?

    \int_0^3 (3x)^{\frac{1}{2}}+1-(x+1)\,dx?

    If so, this is the same as \int_0^3 \sqrt{3}x^{\frac{1}{2}}-x\,dx

    This becomes \left.\left[\frac{2\sqrt{3}}{3}x^{\frac{3}{2}}-\frac{1}{2}x^2\right]\right|_0^3=\frac{2\sqrt{3}}{3}\cdot 3\sqrt{3}-\frac{9}{2}=6-\frac{9}{2}=\frac{3}{2}=1.5

    Does this make sense?
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  3. #3
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    Ah, thanks. I see what I was doing wrong. I was doing (3x) ^ (3/2) instead of taking the square root of 3. Thanks for the help!
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