integrating sqrt(1-x^2)

luca-deltodesco · 2006-06-17 10:31:48

how would you go about integrating sqrt(1-x^2), ive only covered basic integration of functions like x^0.4 - 2x^3 for the moment, som i wouldnt know where to start with this

roah · 2006-06-19 00:37:18

if the integral is from (-1) to (1) you can use geometric interpretation. y^2+x^2=1 => y=sqrt(1-x^2) => a circle (a half of)
pi/2

krassi_holmz · 2006-07-22 21:29:32

Last edited by krassi_holmz (2006-07-22 21:31:07)

mikau · 2006-07-23 10:09:26

this requires a trigonometric substitution. Or perhaps familarity with the derivitives of inverse trig functions. Did you come across this problem in your book/course? Or are you just curious?

Krasi, the thing that always bothers me with trig sub integration... I assume you let x = sin θ, but replacing cos θ with sqrt ( 1 - sin^2) is not necessarily a valid substitution. How can we get away with that?

Last edited by mikau (2006-07-23 10:14:30)

George,Y · 2006-07-23 18:46:34

You asked a very complexed question, luca. It involves virtuely every technique in integration.

#3 +C

luca-deltodesco · 2006-07-23 19:58:33

i was actually hoping the answer wouldnt involve any trigometric functions, i looked up more integeration methods like inverse chain rule method and stuff, but they either didnt work for this, or gave one with trigometric functions

krassi_holmz · 2006-07-23 20:30:15

The arcsin() function is commonly used for integration.

Math Is Fun Forum

#1 2006-06-17 10:31:48

integrating sqrt(1-x^2)

#2 2006-06-19 00:37:18

Re: integrating sqrt(1-x^2)

#3 2006-07-22 21:29:32

Re: integrating sqrt(1-x^2)

#4 2006-07-23 10:09:26

Re: integrating sqrt(1-x^2)

#5 2006-07-23 18:46:34

Re: integrating sqrt(1-x^2)

#6 2006-07-23 19:58:33

Re: integrating sqrt(1-x^2)

#7 2006-07-23 20:30:15

Re: integrating sqrt(1-x^2)

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