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Homework Help: 2 of evaluating definite integrals

  1. Jul 21, 2008 #1
    1. The problem statement, all variables and given/known data
    1)Evaluate the definite integral using FTC:
    [tex] \int_1^4 \left( \frac{d}{dt} \sqrt{4+3t^4} \right)dt [/tex]

    2)Evaluate the definite integral:
    [tex] \int_{-2}^6 f(x)dx [/tex]

    {x if x<1}
    {1/x if x>=1}

    2. Relevant equations

    3. The attempt at a solution
    Having trouble getting the anti-derivative it seems...
    1)[tex] \int_1^4 \sqrt{4} + \int_1^4 \sqrt{3t^4} [/tex]

    [tex] 2\int_1^4 1 + \sqrt{3} \int_1^4 t^2 [/tex]

    [tex] 2x + \sqrt{3} \frac {t^3}{3} [/tex]

    2)[tex] \int_{-2}^0 x + \int_1^6 \frac {1}{x} [/tex]

    [tex] \int_{-2}^0 \frac {1}{2}x^2 + \int_1^6 \ln \abs{x} [/tex]

    Anyways, I hope someone answers :\...took quite some time learning the tex format.
  2. jcsd
  3. Jul 21, 2008 #2
    I figured them both out!
  4. Jul 21, 2008 #3


    User Avatar
    Homework Helper

    For one thing, you only need observe that the question asks you to find the anti-derivative of a derivative. Your approach appears correct but a little off. You appear to have improperly split up the square root term. [tex]\sqrt{a+b} \neq \sqrt{a} + \sqrt{b}[/tex].

    You're forgetting the interval for 0<x<1.

    EDIT: Two minutes too late...
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