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# integration by parts watch

1. 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
2. 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!!
3. 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
4. (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
5. (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.
6. (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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