kingjewel1 Posted January 9, 2005 Share Posted January 9, 2005 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 Link to comment Share on other sites More sharing options...
The Rebel Posted January 9, 2005 Share Posted January 9, 2005 y=(-x^2+1)^1/2How 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 Link to comment Share on other sites More sharing options...
kingjewel1 Posted January 10, 2005 Author Share Posted January 10, 2005 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? Link to comment Share on other sites More sharing options...
The Rebel Posted January 10, 2005 Share Posted January 10, 2005 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. Link to comment Share on other sites More sharing options...
Dave Posted January 11, 2005 Share Posted January 11, 2005 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. Link to comment Share on other sites More sharing options...
kingjewel1 Posted January 11, 2005 Author Share Posted January 11, 2005 Great stuff! I'll keep it in mind. Link to comment Share on other sites More sharing options...
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