C4 Trig. Integration Question

This question (Q64) is from the review exercise in the Edexcel textbook.

I managed to do part (a) fine and got (xsin2x)/2 + (cos2x)/4 + c as the answer.

How do you do part b?

Thanks in advance :smile:

Reply 1

TeeEm

19

Original post by jasminetwine

This question (Q64) is from the review exercise in the Edexcel textbook.

I managed to do part (a) fine and got (xsin2x)/2 + (cos2x)/4 + c as the answer.

How do you do part b?

Thanks in advance :smile:

Use the hint they give you !

Reply 2

Zacken

22

Original post by jasminetwine

This question (Q64) is from the review exercise in the Edexcel textbook.

I managed to do part (a) fine and got (xsin2x)/2 + (cos2x)/4 + c as the answer.

How do you do part b?

Thanks in advance :smile:

You can write you integral as

\displaystyle \int x \left(\frac{\cos 2x + 1}{2}\right) \, \mathrm{d}x

by re-arranging the given identity. This should now be easy to integrate using the answer for your first part.

Reply 3

WhiteGroupMaths

9

Original post by Zacken

You can write you integral as

\displaystyle \int x \left(\frac{\cos 2x + 1}{2}\right) \, \mathrm{d}x

by re-arranging the given identity. This should now be easy to integrate using the answer for your first part.

Second that. Dismantle

\displaystyle \int x \left(\frac{\cos 2x + 1}{2}\right) \, \mathrm{d}x

to give

Unparseable latex formula:

\displaystyle \frac{1}{2} \int x \left(cos2x\right) \, \mathrm{d}x + \int \left\frac{x}{2}\right\, \mathrm{d}x

; by inspection the first integral is pretty much about retrieving your answer from part (a) (do remember to multiply by 1/2 though), while the second integral is something super fundamental.

Hope this clarifies. Peace.

Reply 4

jasminetwine

OP

2

Thanks for your help so far guys!

I can see that cos^2(x) = (cos2x+1)/2, using the identity they gave!

Where do you go from there (i.e. How do you 'dismantle' it)?

Thanks :smile:

Reply 5

WhiteGroupMaths

9

Darling I just demonstrated this in my earlier post. Break up the original integral into two parts. Peace.

Reply 6

jasminetwine

OP

2

Original post by WhiteGroupMaths

Second that. Dismantle

\displaystyle \int x \left(\frac{\cos 2x + 1}{2}\right) \, \mathrm{d}x

to give

Unparseable latex formula:

\displaystyle \frac{1}{2} \int x \left(cos2x\right) \, \mathrm{d}x + \int \left\frac{x}{2}\right\, \mathrm{d}x

; by inspection the first integral is pretty much about retrieving your answer from part (a) (do remember to multiply by 1/2 though), while the second integral is something super fundamental.

Hope this clarifies. Peace.