Date: Wed, 16 Nov 1994 08:08:39 -0800 (PST) From: Cornelia Ott Subject: Calculus I came upon a problem a few days ago about integrals. If a "u substitution" is made for different parts of the function, I get different answers. However the back of my book says that only one of the answers is correct. Here is the problem: Integral of secant squared of 3x times tangent of 3x. The problem is that if I substitute "u" for tangent 3x, then my answer is different from when I substitute "u" for secant 3x. My answers are 1/6tangent squared 3x and 1/6 secant squared 3x respectively. Please help me, I'm stuck. Thank you very much 'firstname.lastname@example.org' (The right answer is supposed to be the "u" substitution for secant 3x)
Date: Wed, 16 Nov 1994 11:23:40 -0500 (EST) From: Dr. Ken Subject: Re: Calculus Hello there! What an excellent question! By my reckoning, both of your answers are right. When you do an integral, you always have to remember to attach a "+ C" to the end of your answer. So if your answer is "(Tan^2[3x])/6 + C", remember your trig identity Tan^2 + 1 = Sec^2. What happens when you take a 1/6 from that C and add it to the big fraction? Let us know if you need more help! -- Ken "Dr." Math
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.