Integration by parts trig substitution FP2

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Reply 20

davros

Original post by notnek

By the way this integral is beyond A Level Maths i.e. wouldn't be in an exam.

Now you're making me sad and nostalgic - this used to be a 'standard' A level integral :frown:

Reply 21

Notnek

Original post by Dingooose

Spoiler

That's correct :smile:

And very impressive for a GCSE student.

You can tidy it up a little bit more by multiplying top and bottom by

b^2

Reply 22

Notnek

Original post by davros

Now you're making me sad and nostalgic - this used to be a 'standard' A level integral :frown:

It appears so much in this forum that it's hard to believe that it isn't an A Level integral.

It might be the most common integral question asked here.

Reply 23

Dingooose

Original post by notnek

That's correct :smile:

And very impressive for a GCSE student.

You can tidy it up a little bit more by multiplying top and bottom by

b^2

Thanks! This totally beats my GCSE maths classes. They should bring calculus into the GCSE maths syllabus.

Reply 24

Notnek

Original post by Dingooose

Thanks! This totally beats my GCSE maths classes. They should bring calculus into the GCSE maths syllabus.

Are you doing the Level 2 Further Maths course? It's a nice course for pre-A Level students who need a bigger challenge.

I wish it existed back when I did GCSEs. Year 11 was a boring maths year for me.

Reply 25

Dingooose

Original post by notnek

Nah, my state school is kinda bad in some ways because they don't offer further maths GCSE or course of any kind. They do, however, offer a Level 3 Algebra course which I think I'm taking. And I want to take GCSE further maths somewhere because I already know quite a lot of the content as I've self-taught myself a lot of things.

(edited 8 years ago)

Reply 26

Notnek

Original post by Dingooose

Nah, my state school is kinda bad in some ways because they don't offer further maths GCSE of any kind. They do, however, offer a Level 3 Algebra course which I think I'm taking.

The Level 3 course is better than nothing but probably won't be much of a challenge if you're doing these kinds of integals.

I assume you're learning A Level in your own time?

Reply 27

Dingooose

Original post by notnek

The Level 3 course is better than nothing but probably won't be much of a challenge if you're doing these kinds of integals.

I assume you're learning A Level in your own time?

Yeah, I'm self teaching some stuff. Dabbled around with C1, C2, C3 and FP1 (proof by induction is by far my favourite topic from FP1), but I'm by no means an expert and I don't know these modules inside and out. Though I guess I am learning A level maths in my own time. I should probably worry about my other GCSE subjects a little bit more in truth.

Reply 28

Gome44

Original post by highestmountain

Could anyone help me with this?

Find the integral of

e^{xcosa} * cos(xsina) dx

Supposedly I could use a substitution and take it from there but this one seems a little tricky.
Any help appreciated!

As this is fp2 you could also say that cos(x)=R(e^ix) then integrate using index laws and some rearrangement

Reply 29

Dingooose

Original post by Gome44

As this is fp2 you could also say that cos(x)=R(e^ix) then integrate using index laws and some rearrangement

Could you elaborate on this please? I'm very keen to know what you mean by cos(x)=R(e^ix).

Reply 30

Gome44

Original post by Dingooose

Could you elaborate on this please? I'm very keen to know what you mean by cos(x)=R(e^ix).

The R stands for real part. I cba to latex the solution so I'll just link it from Wikipedia, see example 3
https://en.m.wikipedia.org/wiki/Integration_using_Euler%27s_formula

Reply 31

Dingooose

Original post by Gome44

The R stands for real part. I cba to latex the solution so I'll just link it from Wikipedia, see example 3
https://en.m.wikipedia.org/wiki/Integration_using_Euler%27s_formula

This method is pretty neat!