circle area

[kingjewel1]

y=(-x^2+1)^1/2

How do i integrate this guy from 0 to 1? since the x^2 has a negative constant, would you need to integrate i? like this [ix^3/3+x]

 

OneStone

[The Rebel]

y=(-x^2+1)^1/2

How do i integrate this guy from 0 to 1? since the x^2 has a negative constant' date=' would you need to integrate i? like this [ix^3/3+x']

 

OneStone

 

I'm liking these questions you're giving cos it gives me the chance to refresh my memory on all the stuff I used to do at college on further maths.

 

The answer is basically (0.5x * (1-x^2)^0.5) + 0.5arcsin(x)

 

It's actually a question I did in one of my assignments, so I got the equations for it too. Unfortunately, until I either got my math editor on word working, or learn the maths codes on here a bit better, it would take too long to write.

 

But it involves integration by substitution, where you substitute x for sin v. You also need to know a couple of trig identities like:

cos2x = (cosx)^2-1 and

sin2x = 2sinxcosx.

 

 

EDIT: I've just found a generic formula in one of my old calculus books as follows:

 

int : SQRT(a^2-x^2) = 0.5x * SQRT(a^2-x^2) + 0.5a^2arcsin(x/a)

 

Notice that if we have x equal to the radius (a), the 1st part cancels, leaving 0.5a^2arcsin(a'/a). If we then take the values of a' = -r and r we get:

0.5a^2arcsin(a/a) - 0.5a^2arcsin(-a/a)

=0.5a^2 * pi - 0.5a^2 * -pi = pi * a^2

[kingjewel1]

aww Cheers! I've been trying to figure out a generic formula for the integration of that type!

Yeh, you know; i was just about to fall asleep and then suddenly the meaning of pi popped into my head. I'd previously thought it was easy to approximate by areas of polygons but it just occured to me how i could do it this way.

 

I see you're in london "The Rebel". I'm doing my alevels and was offered a place at UCL to do maths. I'm seriously contemplating taking them up. What do you think? would you recommend it?

[The Rebel]

I see you're in london "The Rebel". I'm doing my alevels and was offered a place at UCL to do maths. I'm seriously contemplating taking them up. What do you think? would you recommend it?

 

To be honest I don't know anything about UCL, so I wouldn't know. I can only suggest looking up some sites of the internet and seeing what the reviews are like.

[Dave]

To be honest I don't know anything about UCL, so I wouldn't know. I can only suggest looking up some sites of the internet and seeing what the reviews are like.

 

UCL's a pretty damn good university for maths. My maths tutor (a very clever man indeed) got his degree from there.

[kingjewel1]

Great stuff! I'll keep it in mind.