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# P3 integration help elpaw! watch

1. I am stuck on 4 sticky questions:

1)

∫(1/√(9- x^2)) dx

Where definite limits are 0 -> 3

2)

∫(1/(9 x^2 +4) dx

Where limits are -∞ -> ∞

3)

∫(1/[√(x(1-x))]) dx

Where limits are 0 -> 1

4)

∫(1/[(1+ x^2)^(3/2)]) dx

As limits 1 -> →∞

I am very much stuck on these trigonometric subsitutition integrations.
2. here's 1,The rest use a similar approach.
Attached Images

3. Is this for edexcel?
4. (Original post by IntegralAnomaly)
here's 1,The rest use a similar approach.
How do we know that X=Sint, the poster hasn't specified the substitution.
5. (Original post by Hexa)
I am stuck on 4 sticky questions:

1)

∫(1/√(9- x^2)) dx

Where definite limits are 0 -> 3
I=∫(1/√(9- x^2)) dx
I=(1/3)∫(1/√(1- (x/3)^2)) dx

let x=3sinu
dx=3cosudu

I=(1/3)∫1/√(1-cos²u).3cosudu
I=∫(1/cosu).cosudu
I=∫1 du
I=u
I=arcsin(x/3){0,3}
I=(arcsin(1) - arcsin(0))
I=π/2 - 0
I=π/2
====
6. (Original post by Bhaal85)
How do we know that X=Sint, the poster hasn't specified the substitution.
It's a standard thing, you use x = sin t so that the root gives you cos t. Though I'm not sure for P3 if you're meant to do it like that.
7. So for 2) Shall I let (9/4)sin u = x?

EDIT: I mean (2/3)sin u =x
8. 2 looked juicy,so here:
Attached Images

9. (Original post by imasillynarb)
Is this for edexcel?
Integration by substitution is in Edexcel P3, but I've always seen them give you the substitution.
10. The first two are standard results that are in the edexcel formula book, for three, complete the square on the denominator as 1/4 - (x - 1)² and use a standard result (or sub (x - 1) = 1/2 siny) etc
11. here's 3:
Attached Images

12. For 4 use x = tanu
13. (Original post by Hexa)
I am stuck on 4 sticky questions:

1)

∫(1/√(9- x^2)) dx

Where definite limits are 0 -> 3

2)

∫(1/(9 x^2 +4) dx

Where limits are -∞ -> ∞

3)

∫(1/[√(x(1-x))]) dx

Where limits are 0 -> 1

4)

∫(1/[(1+ x^2)^(3/2)]) dx

As limits 1 -> →∞

I am very much stuck on these trigonometric subsitutition integrations.
Try and have a go at 4,use the same procedure as for the rest,but think on an identity that will simplify (1+x^2)^(1/2).
14. (Original post by mockel)
Integration by substitution is in Edexcel P3, but I've always seen them give you the substitution.
Yeh integration by substitutions, but Ive never seen any questions like this: ie where you have to use/make your own trig substitutions
15. Thank you so much people. I'm doing OCR btw, and the formulae book does not have the standard results.
16. these type of questions on edexcel will most prob be p5.If it comes up on p3,then they will tell u the relevent substitution.
17. Unlucky me then, I'm on the rather tougher regieme.

What subsitiution for this integral? (no need for answers, hints only)

∫(1/(x √(x^2 -1)) dx

as definite limits: 1 -> ∞
18. (Original post by Hexa)
Unlucky me then, I'm on the rather tougher regieme.

What subsitiution for this integral? (no need for answers, hints only)

∫(1/(x √(x^2 -1)) dx

as definite limits: 1 -> ∞
think of the hyperbolic functions....................... ........
19. if they're not substitutions, they're standard inverse trigs/hyperbs, which are in the formula book (in edexcel anyway)
20. (Original post by IntegralAnomaly)
think of the hyperbolic functions....................... ........
They might not have covered them in P3 though.

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