It is hard to visualize the bounds of the substitution that will keep it positive but I think that is something I can just memorize from a table. So this is similar to u substitution except that I am not using a single …

2 There are two key things to consider in this example: A good way to try to integrate a function with a square root of a quadratic is to make a trig substitution, since the appropriate trig substitution will get …

Dec 20, 2014 · This doesn't seem to answer OP's question, which asks how to determing a trig or hyperbolic trig substitution is more appropriate (presumably when evaluating integrals), not what …

More to what you asked, any x outside the $\pm a$ range is complex, so having a trig substitution function that is "bounded" is totally appropriate. If you're doing complex integration, have bounds …

But then that means that the substitution is $\alpha=\arccos (x)$ -- however there are many ways to choose inverses to $\cos$ and $\arccos (x)$ is only one of them.

Sep 12, 2025 · Trigonometric substitution does work - and in general for a freshman calculus course, we are very hand-wavy with how we teach the substitution method. We have to also beware of the …

You should use hyperbolic substitution, it is way more convenient than trigonometric here since $\cosh^2-\sinh^2=1$. The inverse hyperbolic functions naturally appear in the final solution.

Jan 25, 2015 · Trig substitution; why can we ignore the absolute value? Ask Question Asked 10 years, 11 months ago Modified 8 years, 6 months ago

How to determine limits of integration for trig substitution? Ask Question Asked 9 years, 10 months ago Modified 9 years, 10 months ago

Mar 16, 2021 · The crux of u-substitution with trigonometric functions is to cancel out an ugly $\sqrt {1-x^2}$ term or $1+x^2$ term. Here, we want to use sine or cosine …