# Calculus 1: Integrals questions and answers

Recent questions in Integrals
uplakanimkk 2022-07-05

### Solving ${\int }_{{x}_{1}}^{{x}_{2}}\frac{dx}{\sqrt{E-{U}_{0}\mathrm{tan}\left(ax{\right)}^{2}}}$

Gauge Terrell 2022-07-04

### How do I solve the following integral ${\int }_{0}^{\mathrm{\infty }}\mathrm{exp}\left(-x\right){\int }_{\sqrt{2kx}}^{\mathrm{\infty }}\mathrm{exp}\left(\frac{-{t}^{2}}{2}\right)\mathrm{d}t\mathrm{d}x$

Frederick Kramer 2022-07-02

### Is there a relationship between $\sum _{n=1}^{\mathrm{\infty }}{\left(\frac{1}{2}\right)}^{n}=1$ and ${\int }_{1}^{\mathrm{\infty }}\frac{1}{{x}^{2}}\phantom{\rule{thinmathspace}{0ex}}dx=1$ ?

nidantasnu 2022-07-02

### How to tackle the integral

Crystal Wheeler 2022-07-02

### Integrate: $\int \sqrt{{x}^{2}-x+1}dx$

Lena Bell 2022-07-01

### How is the integral calculator finding this ${\int }_{0}^{a}\frac{{a}^{2}-{x}^{2}}{\left({a}^{2}+{x}^{2}{\right)}^{2}}dx$ while I get an undefined expression?

2nalfq8 2022-07-01

### I want to evaluate the following integral:${\int }_{-\mathrm{\infty }}^{0}\frac{R}{{\sqrt{{x}^{2}+{R}^{2}}}^{3}}\mathrm{d}x$

cooloicons62 2022-07-01

### I am trying to calculate the integral$\int \frac{dx}{\sqrt[3]{\left(x+1{\right)}^{2}\left(x-1{\right)}^{7}}}.$

Cristopher Knox 2022-06-30

### Lower estimate for ${\int }_{0}^{T}f\left(x\right)\mathrm{sin}f\left(x\right)dx$

Jaqueline Kirby 2022-06-26

### How do I show the following:${\int }_{0}^{\alpha }dx{\int }_{0}^{\alpha }dy\frac{\mathrm{ln}|x-y|}{\sqrt{xy}}=4\alpha \left(\mathrm{ln}\left(\alpha \right)+2\mathrm{ln}\left(2\right)-3\right)$where $\alpha >0$.

Emmy Knox 2022-06-26

### How do I solve ${\int }_{-1}^{1}x{e}^{-{x}^{4}}dx$

Lucille Cummings 2022-06-25

### Series expression of ${\int }_{0}^{\mathrm{\infty }}\frac{{e}^{-x}}{1+{e}^{-x}}dx$

Leah Pope 2022-06-24

### Calculate${\int }_{\mathrm{\partial }F}2xy\phantom{\rule{thinmathspace}{0ex}}dx+{x}^{2}\phantom{\rule{thinmathspace}{0ex}}dy+\left(1+x-z\right)\phantom{\rule{thinmathspace}{0ex}}dz$for the intersection of $z={x}^{2}+{y}^{2}$ and $2x+2y+z=7$. Go clockwise with respect to the origin.

Bailee Short 2022-06-23

### I have the following integral:$I={\int }_{0}^{1}dx\phantom{\rule{thinmathspace}{0ex}}\mathrm{cos}\left({e}^{2\pi ix}\right).$

Roland Waters 2022-06-23

### Solve this integral using the Residue Theorem${\oint }_{C}\frac{{e}^{z}}{\left(z+2\right)\left(z-2\right)}dz$

pokoljitef2 2022-06-22

### I would like to compute the following integral:${\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{{e}^{i\sqrt{{a}^{2}-{x}^{2}}}}{\sqrt{{a}^{2}-{x}^{2}}}\mathrm{d}x\phantom{\rule{1em}{0ex}},\phantom{\rule{1em}{0ex}}a\in \mathbb{R}$

Hailie Blevins 2022-06-22