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 of another …

Jan 24, 2021 · My questions are: What to pick u u when it isn’t as clear? (e.g. How do I come up with the x/4 x / 4?) Are there any tricks to spot it at first glance? Are there practice problems to help me gain …

The substitution rule is always valid, regardless of the substitution made (so long as it is well defined). This is because the theorem that introduces substitutions effectively states "integral A equals integral …

I don't feel qualified to give a full answer, but what's going on is some deep theorems with strong hypotheses, involving pushforward measures for Lebesgue integrals, or more simply a differentiable …

Apr 11, 2021 · I particularly think this is a good idea if your substitution is of the form $u=f (x)$ for some function $f (x)$, as to find the bounds for $u$ will then be very simple.

I know that u u would be equal to 25 −x2 25 x 2 and du d u would equal −2xdx 2 x d x. Then you would pull the −1/2 1 / 2 out front and then integrate u u to 23u3/2 2 3 u 3 / 2. I'm getting confused because …

Dec 4, 2023 · Substitution in double integrals. When can I substitute the same way as in one-variable integrals, and when do I need to use the jacobian?

Oct 28, 2020 · What happens if the greater limit becomes smaller when you change them for u-substitution? Ask Question Asked 5 years, 2 months ago Modified 3 years, 8 months ago

Feb 8, 2024 · So knowing that these functions are there behind the scenes, you can manipulate differentials in confidence that your calculations are valid. This works for integration by substitution, …

Oct 9, 2018 · For u-substitution of a definite integral, is it acceptable to have the limits (bounds) of the new integral equal to one another?