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Math Help - Evaluate the definite integral. Calculous

  1. #1
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    Evaluate the definite integral. Calculous

    need help. I know i got the wrong answer, because i checked in the back of the book, but i have no idea where i messed up. help please

    sinx/((1+cosx)^2)dx from the intervals 0 to pie/3
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  2. #2
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    Re: Evaluate the definite integral. Calculous

    It's hard to know where you messed up without seeing your work, but I would try the substitution:

    u=1+\cos(x)\,\therefore\,du=-\sin(x)\,dx and the integral becomes:

    -\int_{u(0)}^{u\left(\frac{\pi}{3} \right)}u^{-2}\,du=\int_{\frac{3}{2}}^2 u^{-2}\,du

    Can you proceed from here?
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  3. #3
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    Re: Evaluate the definite integral. Calculous

    yes thank you very much!!! I messed up on the anti derivative of cosx. I forgot to add the negative. Thank you.
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    Re: Evaluate the definite integral. Calculous

    Isn't cos(pi/3) = 1/2? Where did you get the 3/2?
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    Re: Evaluate the definite integral. Calculous

    you have to add the 1. u= 1 +cosx.
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    Re: Evaluate the definite integral. Calculous

    the 3/2? not the 2..
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    Re: Evaluate the definite integral. Calculous

    ok so to get the 2 you need to plug the 0 to the equation 1+cosx and that gives you 2. to get the 3/2 you plug in pi/3 to the same formula and that gives you 3/2. the reason that the 2 and the 3/2 switch is because there is a negative in the front and that is a rule.
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    Re: Evaluate the definite integral. Calculous

    Sorry forgot about the 1 lol
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    Re: Evaluate the definite integral. Calculous

    What did you get for your answer?
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    Re: Evaluate the definite integral. Calculous

    i got 1/6
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    Re: Evaluate the definite integral. Calculous

    You dont have to change the U values and flip the b, a. You could just evaluate the integrand and plug in your original values.
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    Re: Evaluate the definite integral. Calculous

    Yes, I just like for the limits of integration to be in ascending order.
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  13. #13
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    Re: Evaluate the definite integral. Calculous

    Yeah I see how it works out. And also I figured out how it works out on the other problem
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