x Turn on thread page Beta
 You are Here: Home >< Maths

# A few more P3 integrals watch

1. OK - for some reason I can't get these ones - i know I should, but my mind just ain't focusing.

1) Integral of x/(x-1)^1/2 dx

2) Integral of cos 2x sin x dx

For number 2, I've been using the substitution u = sin x, so that dx will then equal du/cos x. But which identity do I use for cos 2x?
I'd appreciate some help, so I can get back on track. Cheers.
2. (Original post by foowise)
OK - for some reason I can't get these ones - i know I should, but my mind just ain't focusing.

1) Integral of x/(x-1)^1/2 dx

2) Integral of cos 2x sin x dx

For number 2, I've been using the substitution u = sin x, so that dx will then equal du/cos x. But which identity do I use for cos 2x?
I'd appreciate some help, so I can get back on track. Cheers.
1) You'll have to use integration by parts. differentiate 'x' so it dissapears and integrate '(x-1)^-1/2'

2) Don't use a substitution, just turn cos2X into (2Cos^2x - 1), sub it in and you're there.
3. OK - these might seem dumb - but could you please post your methods?
4. For question number 2, i would use:

cos2x = 2cos^2x - 1

so you would get INT (2cos^2x - 1)sinx
Expanding brackets would give you:

INT 2cox^2xsinx - sinx

for integral of 2cox^2xsinx, use substitution method where u=cos x

for integral of sinx, use normal trig integration.

Hope this helps
5. Here's my method on an attatchment.
Attached Files
6. Maths solutions.doc (23.5 KB, 78 views)
7. (Original post by foowise)
OK - for some reason I can't get these ones - i know I should, but my mind just ain't focusing.

1) Integral of x/(x-1)^1/2 dx

2) Integral of cos 2x sin x dx

For number 2, I've been using the substitution u = sin x, so that dx will then equal du/cos x. But which identity do I use for cos 2x?
I'd appreciate some help, so I can get back on track. Cheers.
If you want to take a slightly different approach, take the trigonometric identity of sinA-sinB=2cos[(A+B)/2]sin[(A-B)/2] (it's in the formula book)
Select two appropriate values for A and B (let A=3x and B=x) and we have:
sin3x-sinx=2cos2xsinx
And so cos2xsinx=o.5sin3x-0.5sinx which is easy to integrate.

1000th post
8. OK - thanx guys.

For number 1 - i used the fact that d/dx(cos^3 x) is -3 cos^2 x sin x to integrate the 2 sin x cos^2 x bit. I'm assuming that is ok (?), since the answer came out right.

But Mysticmin - apparently the answer for number 2 is 2/3(x+2)(x-1)^(1/2)? It's number 26 in Ex 4E in the P3 textbook. I can't see where they get the (x+2) bracket from.
9. (Original post by foowise)
OK - thanx guys.

For number 1 - i used the fact that d/dx(cos^3 x) is -3 cos^2 x sin x to integrate the 2 sin x cos^2 x bit. I'm assuming that is ok (?), since the answer came out right.

But Mysticmin - apparently the answer for number 2 is 2/3(x+2)(x-1)^(1/2)? It's number 26 in Ex 4E in the P3 textbook.
Yeah, the answer you quoted was the same as the one I got, you take a
(x-1)^1/2 outside the bracket as it's a common factor of both terms and you get that answer.
10. OK thanx! God, I am a right royal retard - and to think I'm taking the exam tomorrow. But first, I need a break.

Cheers again.
11. (Original post by foowise)
OK - for some reason I can't get these ones - i know I should, but my mind just ain't focusing.

1) Integral of x/(x-1)^1/2 dx

2) Integral of cos 2x sin x dx

For number 2, I've been using the substitution u = sin x, so that dx will then equal du/cos x. But which identity do I use for cos 2x?
I'd appreciate some help, so I can get back on track. Cheers.
{x/x-1^1/2 . dx
let U = x - 1
du/dx = 1 , dx = 1
x = u + 1

{ u + 1/ u^1/2 .dx = { u/u^1/2 + 1/U^1/2 .dx

{ u + u^-1/2 .dx = u^2/2 + u^1/2/2 + c

(x - 1)^2/2 + (x - 1)^1/2/2 + c
Im not sure though.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 8, 2004
Today on TSR

### How much will your degree earn you?

Find out where yours ranks...

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams