# Integral (9-4x^2)^1/2

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1. Jul 18, 2015

### Phil Frehz

• Member warned about posting with no template
Hey everyone, I'm currently studying for Calc 3 and came across this integral that his been racking my brain beyond insanity. I know the solution is easier than it is. I have looked online and come across substituting to have x=2sin(theta).

I also came across a step where you substitute u for 2x leaving you with:

integral of (25-u2)1/2

I feel like there is a simpler way to solve it but I can't seem to see it

Any help will greatly be appreciated.

2. Jul 18, 2015

### Staff: Mentor

This problem begs to be solved by trig substitution. Try $x=\frac{3}{2}\sinθ$, and then see if you can figure out why it works so well.

Chet

3. Jul 18, 2015

### Qwertywerty

Substitute x= (3/2)×sin(θ) .

4. Jul 18, 2015

### SteamKing

Staff Emeritus
It's not clear that making the substitution u = 2x into (9 - 4x2)1/2 leads to (25 - u2)1/2.

Have you tried this yourself and worked out the algebra to confirm?

In any event, dust off your trig identity knowledge. I'm not saying that the substitution x = 2 sin θ is correct here, but trig substitution is one way to go.

5. Jul 18, 2015

### Phil Frehz

Alright I posted some of the work but I'm having trouble with the dx and d(theta).

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6. Jul 18, 2015

### Qwertywerty

You haven't substituted correctly for dx .

7. Jul 18, 2015

### Qwertywerty

Also you need to now change the limits of your integral .

8. Jul 18, 2015

### Phil Frehz

Forgot to change the limits but I think I correctly included dx as d(theta)

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9. Jul 18, 2015

### Qwertywerty

You are supposed to substitute dx by (3/2)×cos(θ).dθ

10. Jul 18, 2015

### Phil Frehz

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11. Jul 18, 2015

### Qwertywerty

So now just change your limits and you will get the answer .

12. Jul 18, 2015

### Phil Frehz

Alright great got it!!!! Thanks for the help everyone.