# Theta ranges for trig substitution

My professor, when doing trig substitution in lecture, always defines theta between certain intervals and when he takes the square root, he adds an absolute value bar to the trig function and then makes sure its positive through the interval. For practical purposes, is it necessary to go through all that hassle or might I trip up on a problem If I ignore theta ranges and take square roots normally, will I always get the right answer?

arildno
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"If I ignore theta ranges and take square roots normally, will I always get the right answer? "

No, you won't.

can you give me an example? All the indefinite integrals I encountered, through his exercises as well as in high school, all worked without labeling the theta ranges.

mathman
Following through the standard recipe of finding this, we arrive at the integral $$c \int_0^{2\pi} \sqrt{\cos^2\left(\frac{\theta}{2}\right)}\,d\theta,$$ where ##c## is a constant.