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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
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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
Last edited by krassi_holmz (2006-07-22 21:31:07)
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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)
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You asked a very complexed question, luca. It involves virtuely every technique in integration.
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X'(y-Xβ)=0
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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
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The arcsin() function is commonly used for integration.
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