Integrate x^2+1 from 0 to 1

\int_{0}^{1}\left(x^2+1\right)dx

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asin
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Answer

$\frac{4}{3}$

Step by step solution

Problem

$\int_{0}^{1}\left(x^2+1\right)dx$
1

The integral of a sum of two or more functions is equal to the sum of their integrals

$\int_{0}^{1}1dx+\int_{0}^{1} x^2dx$
2

The integral of a constant is equal to the constant times the integral's variable

$\left[x\right]_{0}^{1}+\int_{0}^{1} x^2dx$
3

Evaluate the definite integral

$\int_{0}^{1} x^2dx+0\left(-1\right)+1$
4

Any expression multiplied by $0$ is equal to $0$

$\int_{0}^{1} x^2dx+0+1$
5

Add the values $1$ and $0$

$\int_{0}^{1} x^2dx+1$
6

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$\left[\frac{x^{3}}{3}\right]_{0}^{1}+1$
7

Evaluate the definite integral

$1+\frac{0^{3}}{3}\left(-1\right)+\frac{1^{3}}{3}$
8

Calculate the power

$1+\frac{0}{3}\left(-1\right)+\frac{1}{3}$
9

Divide $1$ by $3$

$1+0\left(-1\right)+0.3333$
10

Any expression multiplied by $0$ is equal to $0$

$1+0+0.3333$
11

Add the values $1$ and $\frac{1}{3}$

$\frac{4}{3}$

Answer

$\frac{4}{3}$

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Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.21 seconds

Views:

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