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Integration help (any help is better than none!) Watch

1. I'm only asking this here because I can't think of anyone else I can possibly ask, so hopefully someone can help me.
I always thought I was good at maths, but obviously not.

Anyway, there are two questions I'm struggling with.

1)Evaluate∫(cosπx/2)dx with limits from 0-1

2) Evaluate
∫dx/(x+1)^1/2 with limits from 0-3

The first one has me completely lost, like I genuinely have no idea where to begin, we've never been shown anything like that in class.

The second one has me a bit baffled, but also wondering if it's a typo or just another way of typing "with respect to x," however I've never seen it written with the dx as the numerator and everything else as the denominator.

If anyone can help with anything, then you'd be a life saver because I'm about to crack my head off of a wall.
2. Is the first one

If so try differentiating
3. (Original post by TenOfThem)
Is the first one

If so try integrating
Yeah that's the first one, although I'm going to make myself sound like an idiot here,
1) how would integrating sin(πx/2) help with cos(πx/2)?
and 2) I still don't know how I'd even go about doing that. It's the πx/2 that's throwing me off. I'm sure it's really simple once I know how, but my issue is that I don't know how to start with, haha. Urgh I feel so stupid trying to figure this out!
4. (Original post by angelooo)

1) how would integrating sin(πx/2) help with cos(πx/2)?
!
ooops see edit
5. (Original post by angelooo)
It's the πx/2 that's throwing me off.
Can you do as the method is the same
6. (Original post by angelooo)
Yeah that's the first one, although I'm going to make myself sound like an idiot here,
1) how would integrating sin(πx/2) help with cos(πx/2)?
and 2) I still don't know how I'd even go about doing that. It's the πx/2 that's throwing me off. I'm sure it's really simple once I know how, but my issue is that I don't know how to start with, haha. Urgh I feel so stupid trying to figure this out!
7. For question 2, another way of writing that, which i find clearer would be

1/ (x+1)^1/2 x dx

then its been put into the form of any other integral you are used to?
Hope that makes sense, i don't know how to do the integral signs etc :P
8. (Original post by TheHaylio)
F

1/ (x+1)^1/2 x dx
Where does this x come from
9. (Original post by TenOfThem)
Where does this x come from
meant to be a multiplied sign sorry
10. (Original post by TenOfThem)
Can you do as the method is the same
Would that be 1/3sin3x+c?
Sorry, I obviously have no idea how to insert equations here either.

I know the chain rule for standard integrals, but I think the fraction is just throwing me a bit.

cos (ax+b) dx = 1/a sin (ax+b) + x

so in my problem, would a = πx? or would a = πx/2? or am I still totally wrong?

Thanks for this btw!
11. (Original post by TheHaylio)
For question 2, another way of writing that, which i find clearer would be

1/ (x+1)^1/2 x dx

then its been put into the form of any other integral you are used to?
Hope that makes sense, i don't know how to do the integral signs etc :P
Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

If that's right, then you've honestly just made my day hahaha
12. (Original post by angelooo)
Would that be 1/3sin3x+c?
Yes, essentially you just divide by the constant and in your question the constant will be
13. (Original post by angelooo)
Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

If that's right, then you've honestly just made my day hahaha
Yes

14. (Original post by angelooo)
Yes that's exactly what I thought it meant, but I wasn't sure if it was a totally different problem or just another way of writing it. So let me get this right, even if the dx is a numerator to what I'm trying to integrate, it still means I'm just integrating it with respect to x, yeah?

If that's right, then you've honestly just made my day hahaha
Yep
hhaha, good!
15. (Original post by TheHaylio)
meant to be a multiplied sign sorry
http://www.numberempire.com/texequat...tioneditor.php

use that, it prevents ambiguous equations and saves time having to learning how to use latex

just copy and paste the expression
16. I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!
17. (Original post by TenOfThem)
Yes

Looks so much better with the symbals :P
18. (Original post by upthegunners)
http://www.numberempire.com/texequat...tioneditor.php

use that, it prevents ambiguous equations and saves time having to learning how to use latex

just copy and paste the expression
Thanks!
19. (Original post by angelooo)
I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!
Haha! Thats okay, i always end up asking for help here- it's good to be able to actually give some help back for once!
20. (Original post by angelooo)
I wish I could give all a big cuddle or something to show my gratitude! I also wish I'd come here when I was first struggling for help because it would've saved a massive headache hahaha. Thanks so much everyone, you're all stars!
NP

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