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    Use the substitution y=sin(x) to calculate integral (between 0 and pi/2) of
    e^(sin(x)) * cos(x) dx

    I seem to be stuck in an endless loop of integrating by parts and I don't know how to do it
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    So, firstly differentiate the y=sinx to dy/dx=cosx. Now, when doing substitution you want to get rid of the dx in the origonal problem, so you can rearrange dy/dx=cosx to get dx=dy/cosx.
    Sub this new value of dx in to the prigonal question: e^y * cos(x) * (dy/cos(x)), the two cos(x)'s cancel out. Now, integrate the e^y * dy between the limits of 0 and pi/2. Please let me know if you get the correct answer by doing this, as I am sitting C4 also
    P.S This isn't integration by parts, just by subsitution!
    Oh, and don't forget to change the lmimits according to y=sinx
    My mistake!!
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    Have you copied this down correctly?
    Do you mean e^(sin x) cos(x) dx where you have partly done the substitution?

    In which case, (possibly) you have not completed the substitution. dy/dx=cosx so the integral becomes just e^y dy=e^y between y=0 and y=1.

    = e^1-e^0 = e-1
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    (Original post by nerak99)
    Have you copied this down correctly?
    Do you mean e^(sin x) cos(x) dx where you have partly done the substitution?

    In which case, (possibly) you have not completed the substitution. dy/dx=cosx so the integral becomes just e^y dy=e^y between y=0 and y=1.

    = e^1-e^0 = e-1
    oops sorry corrected it
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    (Original post by jacksonmeg)
    Use the substitution y=sin(x) to calculate integral (between 0 and pi/2) of
    e^(sin(x)) * cos(x) dx

    I seem to be stuck in an endless loop of integrating by parts and I don't know how to do it
    Using the substitution y = sinx should get rid of the cosx term, so you no longer need to do this by parts.
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    (Original post by AndyW123)
    So, firstly differentiate the y=sinx to dy/dx=cosx. Now, when doing substitution you want to get rid of the dx in the origonal problem, so you can rearrange dy/dx=cosx to get dx=dy/cosx.
    Sub this new value of dx in to the prigonal question: e^y * cos(x) * (dy/cos(x)), the two cos(x)'s cancel out. Now, integrate the e^y * dy between the limits of 0 and pi/2. Please let me know if you get the correct answer by doing this, as I am sitting C4 also
    P.S This isn't integration by parts, just by subsitution!
    Oh, and don't forget to change the lmimits according to y=sinx
    My mistake!!
    Thanks!

    Sad thing is I already did A Level maths and got an A, this is for the first year of my chemistry degree I can't remember any of it lol
 
 
 
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