Recent questions in Integrals

Integral CalculusAnswered question

Davin Ellison 2023-03-14

How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3?

Integral CalculusAnswered question

kennisnetto1h 2023-02-18

How to evaluate $\int \sqrt{{x}^{2}+14x}dx$?

Integral CalculusAnswered question

acainzar3t2 2023-01-20

How to evaluate the integral $\int s\cdot {2}^{s}ds$ ?

Integral CalculusAnswered question

Kayley Kidd 2023-01-06

Integrate the function. $\int x{\mathrm{cos}}^{-1}xdx$

Integral CalculusAnswered question

Arianna Pruitt 2023-01-04

The value of $\underset{x\to {0}^{+}}{lim}\frac{{\mathrm{cos}}^{-1}(x)\cdot {\mathrm{sin}}^{-1}(x)}{x(1-{x}^{2})}$, where [x] denotes the greatest integer $\le x$ is

A) 0

B) $\frac{\pi}{4}$

C) $\frac{\pi}{2}$

D) $\pi $

A) 0

B) $\frac{\pi}{4}$

C) $\frac{\pi}{2}$

D) $\pi $

Integral CalculusAnswered question

Anabella Gilbert 2022-12-23

How to find the integral of $\int {\mathrm{sin}}^{3}xdx$ ?

Integral CalculusAnswered question

Scott Valenzuela 2022-11-29

Find the indefinite integral

$\int {6}^{5x}dx$

$\int {6}^{5x}dx$

Integral CalculusAnswered question

armlanna1sK 2022-11-26

Calculate the double integral.

$\int \int \frac{6x}{1+xy}dA,\text{}R=[0,6]\times [0,1]$

$\int \int \frac{6x}{1+xy}dA,\text{}R=[0,6]\times [0,1]$

Integral CalculusAnswered question

vegetatzz8s 2022-11-24

$1.{\int}_{0}^{\pi}{\int}_{0}^{1}{\int}_{0}^{\sqrt{1-{y}^{2}}}y\mathrm{sin}dydx\phantom{\rule{0ex}{0ex}}\text{Find the above triple integral}$

Integral CalculusAnswered question

Goundoubuf 2022-11-24

How to prove that $\underset{-\pi /2}{\overset{\pi /2}{\int}}\frac{\mathrm{cos}(2x)}{{e}^{x}+1}=0$

Integral CalculusAnswered question

Sophie Marks 2022-11-20

Prove that

${\int}_{0}^{x}{\int}_{0}^{y}{\int}_{0}^{z}f(t)dtdzdy=\frac{1}{2}{\int}_{0}^{x}(x-t{)}^{2}f(t)dt$

${\int}_{0}^{x}{\int}_{0}^{y}{\int}_{0}^{z}f(t)dtdzdy=\frac{1}{2}{\int}_{0}^{x}(x-t{)}^{2}f(t)dt$

Integral CalculusAnswered question

sbrigynt7b 2022-11-20

How to prove that

${\int}_{0}^{1}(1+{x}^{n}{)}^{-1-1/n}dx={2}^{-1/n}$

${\int}_{0}^{1}(1+{x}^{n}{)}^{-1-1/n}dx={2}^{-1/n}$

Integral CalculusAnswered question

Rihanna Bentley 2022-11-17

This problem is giving me a headache.

$\int \frac{4/7+\sqrt{x\sqrt{x}}}{\sqrt{4-x(1+{x}^{3/4})}}\phantom{\rule{thinmathspace}{0ex}}dx$

$\int \frac{4/7+\sqrt{x\sqrt{x}}}{\sqrt{4-x(1+{x}^{3/4})}}\phantom{\rule{thinmathspace}{0ex}}dx$

Integral CalculusAnswered question

Amy Bright 2022-11-14

I need to evaluate the following integral:

$\int {\int}_{G}\frac{\mathrm{ln}({x}^{2}+{y}^{2})}{{x}^{2}+{y}^{2}}dxdy$

$\int {\int}_{G}\frac{\mathrm{ln}({x}^{2}+{y}^{2})}{{x}^{2}+{y}^{2}}dxdy$

Integral CalculusAnswered question

Kyler Oconnor 2022-11-14

How to solve this integration: ${\int}_{0}^{1}\frac{{x}^{2012}}{1+{e}^{x}}dx$

Integral CalculusAnswered question

Jadon Johnson 2022-11-13

I need to prove that

$\underset{n\to \mathrm{\infty}}{lim}{\int}_{0}^{{n}^{2}}n\mathrm{sin}(x/n){e}^{-{x}^{2}}dx=1/2$

$\underset{n\to \mathrm{\infty}}{lim}{\int}_{0}^{{n}^{2}}n\mathrm{sin}(x/n){e}^{-{x}^{2}}dx=1/2$

Although solving integrals starts in high school, these answers that are provided are related to post-secondary problems that are approached by Data Science students, economists, and engineers in their daily tasks. It’s a reason why integral questions that you will see below will span across a wide range of problems. You can also compare your integral problem and see equations that relate to your question. Alternatively, it will help you with solving integrals step by step. There are many methods to do that as the provided answers show. Starting with solving integrals with substitution to variables, the help is there.