Integration TrickDate: 8/13/96 at 16:59:44 From: Anonymous Subject: Integral of Csc (x) f(x)=1/sin(x). What is the indefinite integral of f(x)? I got: F(x)=ln(abs(sin(x))/abs(cos(x)+1))+C But I'm not sure if this is correct. Date: 8/30/96 at 17:30:37 From: Doctor Jerry Subject: Re: Integral of Csc (x) I differentiated and simplified your answer, obtaining 1/sin(x). This shows it is correct. In a table I own, the formula is given this way: integral of csc(x) dx = ln(abs(tan(x/2)))+c I remember this integral from 1950, when I first learned calculus. I liked the trick to do the integration. Just take csc x and multiply it by 1, where 1 = (csc x + cot x)/(csc x + cot x) Then, note that, except for a minus sign, the numerator is the derivative of the denominator. So, one gets -ln(csc x + cot x). This can be written in several different ways. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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