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Integral Problem

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Chen Jang T. | MaCT (Math and Chemistry Tutor)MaCT (Math and Chemistry Tutor)
4.9 4.9 (46 lesson ratings) (46)
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They are essentially the same function. I think both answers should be zero. Only the first integral question utilize more complex approximation, but the answer is not that much different. −1.110223024625157×10−16 = -0.0000000000000001≈0


Pierce O. | Graduate Mathematics Student, Will Tutor Any Math SubjectGraduate Mathematics Student, Will Tutor...
4.7 4.7 (6 lesson ratings) (6)
Hi R,
They are not the same function. If you are unsure, graph them.
Neither integral is difficult to calculate. The first integral, for cos(4x)/(sin(2x)cos(2x)), try looking at ln(sin(2x)cos(2x)), and be sure you remember the trig identity cos(2u)=cos2(u)-sin2(u).
The second integral is just a substitution problem. Best luck


Hi, Pierce.
Thank you very much for your response.

But, I think you made a mistake. You said that they are not the same function and you asked me to graph them.
In fact, I graphed them and found that both of them are really the same function.

We can use any graph program to prove that and we will always get the same result.
I use this site:

However, I appreciate your help.