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Using the Fundamental Theorm of Calculus II to evaluate indefinite integrals

  1. Dec 2, 2008 #1
    1. The problem statement, all variables and given/known data

    Evaluate the following definite integrals using the Fundamental Theorem of Calculus:

    1. 1 [tex]\int[/tex] 4 ( (5x2+7x+5)dx )

    2. -5pi/6 [tex]\int[/tex] 4pi/6 (−6sinx+7cosx) dx )

    3. 2 [tex]\int[/tex] 4 ( (e^-4x)/((e^(-4x))+7) dx )

    If it's unclear, the number on the left is the lower bound of the integral and the number on the right is the upper bound of the integral, followed by the function.

    2. Relevant equations

    a [tex]\int[/tex] b f(x) dx = F(b) - F(a)

    3. The attempt at a solution

    Here are my solutions:

    1. 1157/6

    2. (-6(cos(4pi/6))+7(-sin(4pi/6)))-(-6(cos(-5pi/6))+7(-sin(-5pi/6)))

    3. (4-0.25(log(1+7e^16)))-(4-0.25(log(1+7e^8)))

    --

    It's saying they're all wrong. I can't seem to find where I went wrong. If you could please help me out. Thanks,
     
  2. jcsd
  3. Dec 2, 2008 #2
    I did no 1. and got 172.5 as the solution.
     
  4. Dec 2, 2008 #3
    Thanks - I ended up using my calculator for the sake of this question and its:

    1. 172.5

    2. 11.75833

    3. 0.000011977
     
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