A level Maths Integration Watch

Yodalam
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#1
Report Thread starter 6 months ago
#1
Hi TSR,

I am stuck on this integration question and how to answer it because I have reached a dead end.

y = sin(lnx)

I have integrated it by substitution to get:

pi/2
e^u sin(u)du
0

I then integrated it by parts to get

pi/2
[e^u sin(u)] - e^u cos(u)du
0

I am stuck because I don't know what to do next. If I integrate it again, I will end up repeating myself. Can someone direct me into what I need to do next, please?

Thanks!!!
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ghostwalker
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#2
Report 6 months ago
#2
(Original post by Yodalam)
Hi TSR,

I am stuck on this integration question and how to answer it because I have reached a dead end.

y = sin(lnx)

I have integrated it by substitution to get:

pi/2
e^u sin(u)du
0

I then integrated it by parts to get

pi/2
[e^u sin(u)] - e^u cos(u)du
0

I am stuck because I don't know what to do next. If I integrate it again, I will end up repeating myself. Can someone direct me into what I need to do next, please?

Thanks!!!
When using integration by parts you sometimes need to do it twice.

If we represent your integral by I, then you end up with the situation

I = something - I


Hence 2I = something,

and I = something / 2
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GFSBPBE
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#3
Report 6 months ago
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Use the website 'integral calculator' - it shows steps if you unsure
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Yodalam
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#4
Report Thread starter 6 months ago
#4
Hi,

I have integrated it again and now I have 2 integrals:

e^pi/2
I = [e^u sin(u)] - e^u cos(u)
1


e^pi/2
I = [e^u cos(u)] + e^u sin(u)
1

I don't know what steps to take now? Any help?

Thanks.
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simon0
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#5
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For:

 \displaystyle f(x) = \sin \big( \ln (x) \big) ,

try integration by parts using:

 \displaystyle f(x) = 1 * \sin \big( \ln (x) \big) .

(As "ghostwalker" states, you may need to apply integration by parts twice).
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