Friday, August 12, 2011
How do you evaluate the integral [sqrt(9-x^2)/x]dx?
Since part of this problem is in the form sqrt(a^2-x^2), I've used trigonometric substition by substituting 3sin(theta) for x. Dx is therefore 3cos(theta)d(theta). This means that the integral equals 3cos(theta)/3sin(theta)*3cos(theta)d(the… This equals 3*integral [cos(theta)]^2/sin(theta). This is where I get stuck. I could either call the inside of this integral cot(theta)*cos(theta), or I could substitute [1-sin(theta)^2] for cos(theta)^2 to get csc(theta) - sin(theta). Either way, I'm not quite sure how to integrate the entire integral. Any suggestions? Thanks for your advice! :)
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