Recent questions in Applications of integrals

Applications of integrals
Answered

Salvador Bush
2022-07-03

$\int \frac{1}{({x}^{2}+4x+9)}\phantom{\rule{thinmathspace}{0ex}}dx$

Applications of integrals
Answered

Augustus Acevedo
2022-07-03

Applications of integrals
Answered

hawatajwizp
2022-06-26

Applications of integrals
Answered

Ezekiel Yoder
2022-06-24

I have the next integral:

$\int {\textstyle (}\frac{\mathrm{sin}\frac{1}{x}}{{x}^{2}\sqrt{(4+3\mathrm{sin}\frac{2}{x})}}{\textstyle )}\phantom{\rule{thinmathspace}{0ex}}dx,\phantom{\rule{thickmathspace}{0ex}}x\in {\textstyle (}0,\mathrm{\infty}{\textstyle )}$

I used the substitution $u=\frac{1}{x}$ and I got

$-\int {\textstyle (}\frac{\mathrm{sin}u}{\sqrt{(4+3\mathrm{sin}2u)}}{\textstyle )}\phantom{\rule{thinmathspace}{0ex}}du$

Can somebody give me some tips about what should I do next, please?

Applications of integrals
Answered

Davon Irwin
2022-06-21

$I=\int \frac{\mathrm{sin}3x\cdot \mathrm{sin}\frac{5x}{2}}{\mathrm{sin}\frac{x}{2}}dx$

Brajesh Kumar
2022-06-16

Evaluate double integral of ${\int}_{0}^{1}{\int}_{0}^{x}{e}^{\frac{x}{y}}dxdy$

Applications of integrals
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juanberrio8a
2022-06-16

Applications of integrals
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gnatopoditw
2022-06-14

Applications of integrals
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hanglutuupx6
2022-06-02

Applications of integrals
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Rachel Villa
2022-05-29

Applications of integrals
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Davin Fields
2022-05-26

${\int}_{0}^{\pi}d\theta \mathrm{cos}k\theta \mathrm{cos}n\theta \phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}{\int}_{0}^{\pi}d\theta \mathrm{sin}k\theta \mathrm{sin}n\theta $

I have tried using trigonometric identities to get a general solution but I had no luck understanding the nature of the integrals. If anyone can point out any hints or patterns, it would be much appreciated.

Applications of integrals
Answered

Alisa Durham
2022-05-15

$\int \frac{{\mathrm{sin}}^{3}(x)}{({\mathrm{cos}}^{4}(x)+3{\mathrm{cos}}^{2}(x)+1)\cdot \mathrm{arctan}(\mathrm{sec}(x)+\mathrm{cos}(x))}$

I am unable to manipulate this integral. The actual integral in question is definite with limits from 0 to $\frac{\pi}{2}$, but I feel it can't be calculated without knowing the antiderivative.

My initial try was to take $\mathrm{sec}(x)+\mathrm{cos}(x)$ as t, but It didn't solve.

Applications of integrals
Answered

Kiersten Hodge
2022-05-13

Applications of integrals
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revistasbibxjm87
2022-05-13

Applications of integrals
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encamineu2cki
2022-05-13

Applications of integrals
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zuzogiecwu
2022-05-13

Applications of integrals
Answered

Alisa Durham
2022-05-13

Applications of integrals
Answered

Alisa Durham
2022-05-13

Applications of integrals
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Autumn Pham
2022-05-13

Applications of integrals
Answered

Aedan Gonzales
2022-05-13

Applications of integrals are one of the popular but still complex fields that many students encounter not only in Math and Physics but in subjects like Programming and Engineering. For example, start with the applications of double integrals and you will see how it is useful in the construction of some building where the shape must be found or the gravity matters should be presented as the model. At the same time, if your questions are based on equations, consider geometric applications of definite integrals help that is also present below as you take a look through the relevant answers.