I'm busy studying for my Calculus exam and came across something that I'm not too sure about. The question asks to use z-substitution to determine an integral. The actual question is:
Use z=tan(x/2) to determine the integral:
Integral from 0 to pi/3 of dx/(3+2cosx)
Is Z-Substitution the same as normal substitution but they give you what to use? Or is there another method?
Any help would be appreciated. Thanks in advance!
Answer
This is a standard substitution for evaluating integrals of rational functions of trigonometric functions. A more common name is the Weierstrass substitution.
You will find full details in the Wikipedia article linked to above.
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