Questions tagged [integration]
For questions related to the teaching of integral calculus
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Does this explanation of integration and the Fundamental Theorems of Calculus make any sense?
First, Sue Pemberton (Pure Mathematics 1 Coursebook, 2018, Cambridge University Press) introduces
integration as the reverse process of differentiation ...
$\int x^3 \mathrm d x$ is called the ...
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What is the terminology for "self-referral" integrals in calculus?
In the topic of integration and anti-derivatives in Calculus we come across cases where the attempt at integration by parts brings us back to the original integral, the most basic example being $\int ...
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Antiderivative of $1/x$, with or without absolute value?
Many textbooks include $\int \frac{1}{x} dx = \ln |x| + c$ in their list of antiderivative formulas, with the absolute value. Correspondingly, they do the same with the antiderivative of $\tan x$ or ...
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How to properly define volume for beginner calculus students?
I'm interested in opinions based on experience about how to introduce volume for beginner calculus students. Below I present some observations and specific questions.
In Stewart's book, the volume of ...
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Definite integrals with equal limits
As a property of definite integrals, we teach that definite integrals are zero if the lower and upper limits are the same (Wolfram mathworld says this too). Is this valid in general?
In the case of ...
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Student forgets to remove dx after integrating
I am tutoring another US college student in a Calculus 1 class. Initially, she was having trouble with basic concepts, but after much prodding most of the conceptual difficulties seem to have been ...
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Should an undergraduate math program contain a course on Lebesgue integration?
Is it standard for a math undergraduate program to have a course on Lebesgue integration?
Does Riemann integral suffice for undergraduates?
The reason of my question is I read a paper by Bartle titled ...
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Good Examples of Equations Derived from Elementary Calculus
I'm collecting additional enrichment content for my calculus students. I'm looking for examples of equations that are used in various fields, but which can be derived at least somewhat ...
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Why can an easily graphable definite integral, be labyrinthine to evaluate?
How can I explain to 16-year-olds, who just started calculus, why it's so nettlesome and tricky to symbolically integrate definite integrals, when their graphs look so unremarkable and straightforward?...
user15364
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Usefulness of $u$-substitution in and beyond early Calculus?
My students, when presented with an integral (source) like
$$\int (2x+2)e^{x^2+2x+3} \ dx$$
are apt to recognize derivative patterns like $u' e^{u}$ and reverse-engineer anti-derivatives rather than ...
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Finding an error in a partial integration [closed]
There must be an error in this partial integration but I do not see it. Do you see it?
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Analogy for cylindrical shells
The analogy for cross-sections is easy since we can think of how slices of bread can make up a loaf.
But what would be the analogy for cylindrical shells?
Regarding shapes, apparently there's ...
user13544
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The purpose of a particular rational function integration exercise
This might be a more appropriate question for math.stackexchange, but it's about a problem I'm considering giving my students, so here it goes.
One of the later exercises in Section 7.4 of James ...
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Intuition or geometry for Partial Fractions
When teaching partial fractions, there's probably no way to escape the heavy algebra necessary for partial fractions, but I'm wondering how to introduce the idea in a way that is intuitive or ...
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The hardest case of integration by partial fractions
The context is explaining to calculus students how to integrate rational functions by using partial fractions decomposition.
As we all know, partial fractions decomposition is a method to write every ...
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