Jan 24, 2021 · Just as a general note - integrals are not deterministic like derivatives are. For derivatives, you can have a strict procedure give you the answer. For integrals, not so much. In fact, …

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 …

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?

Feb 4, 2014 · Then you would pull the $-1/2$ out front and then integrate $u$ to $\frac {2} {3}u^3/2$. I'm getting confused because the answer key changed the bounds to $25$ to $0$.

Dec 4, 2023 · I approached it initially using traditional u-substitution similar to one-dimensional integrals. Surprisingly, it yielded the correct result, but as I delved deeper into my textbook, I discovered a …

Feb 8, 2024 · This is a result you can prove, and is typical in analysis classes (where one gets keener on the mild abuse of convention in the indefinite case), but is essentially just application of the chain …

I want to solve the following integral: $$\\int_{-2}^2 \\sqrt{4- x^2} dx$$ I am thinking of doing a u-substitution of the whole term inside the root. If I do this, I need to change the limits of the

Sep 24, 2022 · 0 For most integrals I have came across, u is almost always substituted in the denominator. However, I came across the following integral: $$\int\frac {\sqrt {x}} {1+x}dx$$ I …

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 …

Jul 16, 2014 · I've highlighted the part I don't understand in red. Why do we change the limits of integration here? What difference does it make? Source of Quotation: Calculus: Early …