Method to Integrate sqrt(1-x^2)Date: 9/11/96 at 16:21:20 From: Anonymous Subject: Method to Integrate sqrt(1-x^2) What is the integral of [sqrt(1-x^2)]dx from [-1,1]? Date: 9/12/96 at 0:21:33 From: Doctor Pete Subject: Re: Method to Integrate sqrt(1-x^2) Hint: Use a trigonometric substitution of the form x = f(u), dx = f'(u) du. Also, you might want to remember the identity (Cos[x]^2) = (1+Cos[2x])/2, which comes from the half-angle formula Cos[x/2] = Sqrt[(1+Cos[x])/2] . This method will take you through two substitutions, the second of which is obvious. Apply the limits after you find the indefinite integral in terms of your original variable x, or alternatively, you can apply the substitutions to the limits as you go. If you need more help, feel free to ask. -Doctor Pete, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 9/13/96 at 14:5:18 From: Doctor Ceeks Subject: Re: Method to Integrate sqrt(1-x^2) Hi, Another way is to recognize this as the area of the semi-circle of unit radius...so that the answer is pi/2. -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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