# Master Integral Application Problems

Recent questions in Applications of integrals

## 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 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

## 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