Integrate x^3+2 from -1 to 1

\int_{-1}^{1}\left(x^3+2\right)dx

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Answer

$4$

Step by step solution

Problem

$\int_{-1}^{1}\left(x^3+2\right)dx$
1

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

$\int_{-1}^{1}2dx+\int_{-1}^{1} x^3dx$
2

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

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

Evaluate the definite integral

$\int_{-1}^{1} x^3dx-1\left(-1\right)\cdot 2+1\cdot 2$
4

Multiply $2$ times $1$

$\int_{-1}^{1} x^3dx+2+2$
5

Add the values $2$ and $2$

$\int_{-1}^{1} x^3dx+4$
6

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

$\left[\frac{x^{4}}{4}\right]_{-1}^{1}+4$
7

Evaluate the definite integral

$4+\frac{{\left(-1\right)}^{4}}{4}\left(-1\right)+\frac{1^{4}}{4}$
8

Calculate the power

$4+\frac{1}{4}\left(-1\right)+\frac{1}{4}$
9

Divide $1$ by $4$

$4+0.25\left(-1\right)+0.25$
10

Add the values $\frac{1}{4}$ and $4$

$0.25\left(-1\right)+4.25$
11

Multiply $-1$ times $\frac{1}{4}$

$4.25-0.25$
12

Subtract the values $\frac{17}{4}$ and $-\frac{1}{4}$

$4$

Answer

$4$

Problem Analysis

Main topic:

Integral calculus

Time to solve it:

0.24 seconds

Views:

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