 # Master Integral Application Problems

Recent questions in Applications of integrals Injenueengado1zy8 2023-03-24

## How to find the length of a curve in calculus? Davin Ellison 2023-03-11

## How to calculate the right hand and left hand riemann sum using 4 sub intervals of f(x)= 3x on the interval [1,5]? Nicholas Huynh 2023-03-09

## Estimate the area under the curve $f\left(x\right)={x}^{2}$ over the interval [0,10] with 5 strips using Left Riemann Sums? Nola Nunez 2023-02-25

## How to find the arc length of the curve y=ln x over the interval [1,2]? Geobassurseuad5 2023-02-25

## How to find the distance travelled from t=0 to t=1 by a particle whose motion is given by $x=4{\left(1-t\right)}^{\frac{3}{2}},y=2{t}^{\frac{3}{2}}$? Custodio88j 2023-02-02

## How to find the lengths of the curve $y=\frac{{x}^{3}}{12}+\frac{1}{x}$ for $1\le x\le 3$? Rythalltiys 2023-01-27

## How to find the arc length of the curve $f\left(x\right)=\frac{{x}^{3}}{6}+\frac{1}{2x}$ over the interval [1,3]? cleisiogwro 2023-01-26

## How to find the length of the curve for $y=2{x}^{\frac{3}{2}}$ for (0, 4)? Salvador Bush 2022-07-03

## integral substitution not by u-sub$\int \frac{1}{\left({x}^{2}+4x+9\right)}\phantom{\rule{thinmathspace}{0ex}}dx$ Augustus Acevedo 2022-07-03

## I have to integrate this : $\int \frac{{\mathrm{cos}}^{2}\left(x\right)}{1+\mathrm{tan}\left(x\right)}dx$ hawatajwizp 2022-06-26

## How to calculate the integral ${\int }_{0.5}^{1}\frac{1}{\sqrt{2x-{x}^{2}}}$? Ezekiel Yoder 2022-06-24

## Primitive of a function with $\mathrm{sin}\frac{1}{x}$I have the next integral:$\int \left(\frac{\mathrm{sin}\frac{1}{x}}{{x}^{2}\sqrt{\left(4+3\mathrm{sin}\frac{2}{x}\right)}}\right)\phantom{\rule{thinmathspace}{0ex}}dx,\phantom{\rule{thickmathspace}{0ex}}x\in \left(0,\mathrm{\infty }\right)$I used the substitution $u=\frac{1}{x}$ and I got$-\int \left(\frac{\mathrm{sin}u}{\sqrt{\left(4+3\mathrm{sin}2u\right)}}\right)\phantom{\rule{thinmathspace}{0ex}}du$Can somebody give me some tips about what should I do next, please? Davon Irwin 2022-06-21

## Is there any short method to solve the integral$I=\int \frac{\mathrm{sin}3x\cdot \mathrm{sin}\frac{5x}{2}}{\mathrm{sin}\frac{x}{2}}dx$ Brajesh Kumar2022-06-16

## Evaluate double integral of ${\int }_{0}^{1}{\int }_{0}^{x}{e}^{\frac{x}{y}}dxdy$ juanberrio8a 2022-06-16

## Heaviside and trig function integral $\int \mathrm{sin}\left(3t\right)\theta \left(t\right)dt$ gnatopoditw 2022-06-14

## How do I integrate $\frac{{x}^{2}}{\sqrt{9{x}^{2}+15}}$? hanglutuupx6 2022-06-02

## Added angle formula to solve this indefinite integral $\int \frac{2\mathrm{cos}x-\mathrm{sin}x}{3\mathrm{sin}x+5\mathrm{cos}x}\phantom{\rule{thinmathspace}{0ex}}dx$ Rachel Villa 2022-05-29

## Evaluate the definite integral using trig. sub $\int \frac{{x}^{3}}{\sqrt{9-{x}^{2}}}dx$ Davin Fields 2022-05-26
## I do not understand why for the two integrals below, the result is always 0 unless $|k|=n$ , in which case the result is $\pi /2$${\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. Alisa Durham 2022-05-15