Is this in maths curriculum

Is integrating y= sin(ln x) in Edexcel A level Maths curriculum? Found this in a pre 2018 past paper. I have never come across this type of integrating in the text book.

(edited 1 year ago)

Reply 1

mqb2766

Original post by dent58

Is integrating y= sin(ln x) in Edexcel A level Maths curriculum? Found this in a pre 2018 past paper. I have never come across this type of integrating in the text book.

Transformation and/or by parts both of which are on the spec. It would probably be on the harder side, but its only a few lines so not v. hard.

(edited 1 year ago)

Reply 2

dent58

Original post by mqb2766

Transformation and/or by parts both of which are on the spec. It would probably be on the harder side, but its only a few lines so not v. hard.

we are not taught what to do when the function goes on by parts loop

Reply 3

mqb2766

Original post by dent58

we are not taught what to do when the function goes on by parts loop

1*sin(ln(x))
integrate 1 and differentate sin(ln(x)) and its not a loop.

(edited 1 year ago)

Reply 4

dent58

I ended up with xsin(lnx) - ∫ cos(lnx) dx
by parts again,
xsin(lnx) - xcos(lnx) - ∫sin(lnx) dx

Reply 5

mqb2766

Original post by dent58

I ended up with xsin(lnx) - ∫ cos(lnx) dx
by parts again,
xsin(lnx) - xcos(lnx) - ∫sin(lnx) dx

and if you do it again, you get the original integral +
xsin(ln(x)) - xcos(ln(x))
so its 1/2 that value.

Reply 6

dent58

Thanks for explaining! Still not sure if this is in spec though.

Reply 7

mqb2766

Original post by dent58

Thanks for explaining! Still not sure if this is in spec though.

On page 29
https://qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/a-level-l3-mathematics-specification-issue4.pdf
it says IBP can cover more than one application of the method but excludes reduction formulae. Using that definition it would include this question which if you did the transformation at the start it would be equivalent to integrating
e^x * sin(x)
so IBP twice to get back to the starting point and take it over and divide by 2. However, Id imagine this/they would be on the boundary of what you could be asked.