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# C3/C4 kinda question on integration watch

1. I really should remember how to do these..

I've tried the method where you say

But I didn't get very far. It's kinda difficult to explain what I've tried, but if someone could start me off with the method, I would be very thankful.
2. (Original post by Jacob_Heb)
I really should remember how to do these..

I've tried the method where you say

But I didn't get very far. It's kinda difficult to explain what I've tried, but if someone could start me off with the method, I would be very thankful.
Try a substitution of .
Also, don't try to 'learn' the integral.
3. kx isa multiple of the differential of the inside of the bracket, so the integral will just be a cos term
4. (Original post by Farhan.Hanif93)
Try a substitution of .
do you need to do this?
5. (Original post by Mc^3)
do you need to do this?
The OP can clearly not do it by recognition otherwise he wouldn't be trying IBP. I wouldn't need it. Substitution is a far more useful technique to practice than recognition.
6. its just -(k/2pi) cos(pi x^2), +c no?
7. (Original post by Mc^3)
its just -(k/2pi) cos(pi x^2), +c no?
Yes. Not sure why you're giving the answer though?
8. (Original post by Farhan.Hanif93)
The OP can clearly not do it by recognition. I wouldn't need it. Substitution is a far more useful technique to practice than recognition.
IGNORE ME...
9. (Original post by Mc^3)
really? we were always told to do it by inspection if the integral was a product of the form f-dash x times f-x. it worked for me!!
Certainly in this case, even if the OP manages to spot it, he is likely to make a mistake. You may be slightly stronger with maths than the OP, maybe being considerate of that would be a good idea.
10. (Original post by Farhan.Hanif93)
Certainly in this case, even if the OP manages to spot it, he is likely to make a mistake. You may be slightly stronger with maths than the OP, maybe being considerate of that would be a good idea.
my bad, i'm just used to thinking about the quickest way to do things, wasn't trying to make it more difficult/show off! i'm not sure how most people are taught to do these things, our teacher was fairly old-school, and seemed to think C4 was a bit of a doss, and we should do as much as possible by inspection!! there were mixed results
11. (Original post by Mc^3)
my bad, i'm just used to thinking about the quickest way to do things, wasn't trying to make it more difficult/show off! i'm not sure how most people are taught to do these things, our teacher was fairly old-school, and seemed to think C4 was a bit of a doss, and we should do as much as possible by inspection!! there were mixed results
Fair enough. I wasn't having a go!
Just saying that some people may not be as comfortable with maths as you and I.
I was taught recognition for C3 but when it came to C4, I did substitution first, followed by recognition for C4 integrals. Each to their own. There should really be much more of a focus on subs though, it's a far more useful skill than recognition.
12. (Original post by Farhan.Hanif93)
Fair enough. I wasn't having a go!
Just saying that some people may not be as comfortable with maths as you and I.
I was taught recognition for C3 but when it came to C4, I did substitution first, followed by recognition for C4 integrals. Each to their own. There should really be much more of a focus on subs though, it's a far more useful skill than recognition.
yes, although i find its frustrating when they give you (often arcane) substitutions in the exam. i found it made STEP integration more of a shock, when you need to discover a suitable substitution yourself!
13. (Original post by Mc^3)
yes, although i find its frustrating when they give you (often arcane) substitutions in the exam. i found it made STEP integration more of a shock, when you need to discover a suitable substitution yourself!
I absolutely love calculus on STEP, it actually gives you a chance to apply your brain for once. I find I can do most of those questions! Number theory tends to trip me up and occasionally geometry. I quite like the ones on 3D shapes though.
Now we are going a bit off topic, so if you want to continue this convo, PM me.
14. I appreciate the help, but I still don't quite understand. The is as part of the ? Surely I've then ended up with two variables, x and u, with which to integrate with respect to?

I know I'm missing something really simple, but you'll have to forgive me, I'm rusty here.
15. have you done integration by substitution yet? if not, have you been told how to solve these if the thing before the sin term is a multiple of the differential of the inside of the bracket?
16. (Original post by Jacob_Heb)
I appreciate the help, but I still don't quite understand. The is as part of the ? Surely I've then ended up with two variables, x and u, with which to integrate with respect to?

I know I'm missing something really simple, but you'll have to forgive me, I'm rusty here.
Are you familiar with integration by substitution?
I'd imagine you should be if you've seen integration by parts...
The whole point of integration by substitution is to have a change of variable to make the integral easier to deal with.
If you differentiate and make the subject see if any cancelling takes place when you put this in.
17. (Original post by Farhan.Hanif93)
Are you familiar with integration by substitution?
I'd imagine you should be if you've seen integration by parts...
The whole point of integration by substitution is to have a change of variable to make the integral easier to deal with.
If you differentiate and make the subject see if any cancelling takes place when you put this in.

Oh! I have it now! , right?
Thank you both
18. yes
19. (Original post by Jacob_Heb)
Oh! I have it now! , right?
Thank you both

20. Well the question actually asked me to evaluate it between 0 and 1, to which I got , but the indefinate integral was
, I think.

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