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 …

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 …

The key issue is that both the trigonometric and the hyperbolic substitutions lead to simpler integrals, because the irrational integrand becomes a rational function of trigonometric or …

Trigonometric Substitution - Arc Length Ask Question Asked 12 years, 9 months ago Modified 12 years, 9 months ago

These comments apply to any trigonometric (or other) substitutions that involve choices or an apparent dependence of the post-substitution calculations on the choices.

How to determine limits of integration for trig substitution? Ask Question Asked 9 years, 8 months ago Modified 9 years, 8 months ago

U-substitution is for functions that can be written as the product of another function and its derivative. $$\int u du$$ Integration by parts is for functions that can be written as the product …

Jan 25, 2015 · Without reference to $\theta$ substitution two curves can be drawn one above x-axis and another below x-axis. For the former, area under curve is > 0, and for latter, < 0.

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 …

Problem using trigonometric substitution $x = a \sec θ$ and domain of $\theta$ Ask Question Asked 10 years, 3 months ago Modified 9 months ago