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Math Help - Integration question

  1. #1
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    Integration question

    Do I just straight up integrate (x + cosx)? and to change my interval do I plug Pi/2 and Pi/3 to cos(x)??
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  2. #2
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    Re: Integration question

    Quote Originally Posted by asilvester635 View Post
    Do I just straight up integrate (x + cosx)? <--- yes
    and to change my interval do I plug Pi/2 and Pi/3 to cos(x)??<--- no, you have to replace x by pi/2 and pi/3 respectively
    .....

    Spoiler:
    You should come out with
    \int_{\frac \pi3}^{\frac \pi2}(x+\cos(x)) dx = \left[\frac12 x^2 + \sin(x) \right]_{\frac \pi3}^{\frac \pi2}= \left(\frac{\pi^2}8+1\right) - \left(\frac{\pi^2}{18}+\frac12 \cdot \sqrt{3} \right)
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  3. #3
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    Re: Integration question

    awesome... so we didn't have to change the interval of Pi/2 and Pi/3, because usually that's what I'm used to doing..... So since we can't further simplify this equation we just leave it as it is??
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Integration question

    You only change the limits of integration if you have made a substitution. Then you write those limits in terms of the new variable.
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  5. #5
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    Re: Integration question

    Sometimes when I'm doing a substitution on a definite integral, I'll write \int_{x=a}^{x=b}f(x)\ dx so that I remember to change the limits of integration when I do the substitution.

    - Hollywood
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