Questions tagged [integration]

For questions about the properties of integrals. Use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that describe the type of integral being considered. This tag often goes along with the (calculus) tag.

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$I_n=\int_{0}^{1} \arcsin(1-x^n) \,dx$ [closed]

Find the limit of the sequence $(I_n) _n$ wherw $I_n=\int_{0}^{1} \arcsin(1-x^n) \,dx$. I try to integrate by parts but I get $\infty \cdot 0$. I need to practice more examples. Can you recommend ...
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Confused by many different definitions of antiderivative

Wikipedia: an antiderivative ... of a function $f$ is a differentiable function $F$ whose derivative is equal to the original function $f$. This can be stated symbolically as $F' = f$. Stewart, ...
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Does $\int_1^{\infty } w \sin (w) \, dw$ converge? [duplicate]

Can you help me to show if this integral converges or diverges? $$\int_1^{\infty } w \sin (w) \, dw$$ It oscillates infinitely. Edits: I deleted the plot since the scale was not correct. I also ...
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How do I approach this volume problem?

I'm trying to find the volume of a body bounded by the surface given by the equation $(x^2 + y^2 + z^2)^2 = (x^2 - y^2)z$, where $z \geqslant 0$. Here's my thought process: by observing that the we ...
1 vote
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Excess part from integration of graph

Photo of Graph of a arbitrary function on which integration is performed Here, in the photo, using the basic idea of integration, we make a long rectangular block to cover the area under the graph. ...
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Arc length derivation [closed]

enter image description here Why does the hypothetical X value Xi that would equal the avg slope of a section get replaced by X? I don't remember using the mean value theorem in the definition of the ...
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$A = \{ x^2 + y^2 + z^2 < 2x + 2y \} \subset \mathbb{R}^3$.Calculate $\int_A xyz \ d \lambda_3$. I need to verify my solution.

$A = \{ x^2 + y^2 + z^2 < 2x + 2y \} \subset \mathbb{R}^3$ Calculate: $$\int_A xyz \ d \lambda_3$$ Solution: We know that: $x^2 + y^2 + z^2 > 0$ and therefore $2x + 2y > 0 \iff x + y > 0$ ...
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Conditions for function to be periodic

I am investigating the following type of functions $$I(\alpha) = \int_{0}^{\pi}f(t)\cos(\alpha t)\,\mathrm{d}t\,.$$ where $f(t)$ is a real-valued function with non-negative ...
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Will the following Method of engineering analysis work?

Analytical Engineering Analysis of 3D Shapes Using volume integral($\iiint_{}^{}{f(t)}dx dy dz$) to do a Analytical Engineering Analysis of 3D Shapes without using mesh based FEA. Like integration ...
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Approximation or an analytical form of integrals

I'm working on a bayesian rule of wavelet shrinkage using the raised cosine distribution as a prior distribution for $\theta$. Its expression is given by: \delta(d) = \frac{(1-\alpha) \int_{\frac{-\...
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A simple yet complex proof that I am unable to solve. [closed]

prove that: ((e^(ax ))cos(bx))^n=((sqrt(a^2+b^2))^n)(e^(ax))cos(bx + n.arctan(b/a))
Say we have two compactly supported functions $f,g:\mathbb{R}^n\to\mathbb{R}$. I found myself computing \begin{split} \int_{\mathbb{R}^n}f\frac{\partial^{r}g}{\partial x^{\alpha_1}\...