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here's 1,The rest use a similar approach.
Reply 2
Is this for edexcel?
Reply 3
IntegralAnomaly
here's 1,The rest use a similar approach.


How do we know that X=Sint, the poster hasn't specified the substitution.
Reply 4
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
====
Reply 5
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.
Reply 6
So for 2) Shall I let (9/4)sin u = x?

EDIT: I mean (2/3)sin u =x
2 looked juicy,so here:
Reply 8
imasillynarb
Is this for edexcel?


Integration by substitution is in Edexcel P3, but I've always seen them give you the substitution.
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
here's 3:
For 4 use x = tanu
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).
Reply 13
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
Reply 14
Thank you so much people. I'm doing OCR btw, and the formulae book does not have the standard results.
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.
Reply 16
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 -> ∞
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...............................
Reply 18
if they're not substitutions, they're standard inverse trigs/hyperbs, which are in the formula book (in edexcel anyway)
Reply 19
IntegralAnomaly
think of the hyperbolic functions...............................


They might not have covered them in P3 though.

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