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# Definite Integrals Calculator

## Get detailed solutions to your math problems with our Definite Integrals step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of definite integrals. This solution was automatically generated by our smart calculator:

$\int_0^2\left(x^4+2x^2-5\right)dx$
2

Expand the integral $\int_{0}^{2}\left(x^4+2x^2-5\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

$\int_{0}^{2} x^4dx+\int_{0}^{2}2x^2dx+\int_{0}^{2}-5dx$

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $4$

$\left[\frac{x^{5}}{5}\right]_{0}^{2}$

Evaluate the definite integral

$\frac{2^{5}}{5}- \frac{0^{5}}{5}$

Simplify the expression

$\frac{32}{5}$
3

The integral $\int_{0}^{2} x^4dx$ results in: $\frac{32}{5}$

$\frac{32}{5}$

The integral of a constant times a function is equal to the constant multiplied by the integral of the function

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

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $2$

$2\left[\frac{x^{3}}{3}\right]_{0}^{2}$

Evaluate the definite integral

$2\cdot \left(\frac{2^{3}}{3}- \frac{0^{3}}{3}\right)$

Simplify the expression

$\frac{16}{3}$
4

The integral $\int_{0}^{2}2x^2dx$ results in: $\frac{16}{3}$

$\frac{16}{3}$

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

$\left[-5x\right]_{0}^{2}$

Evaluate the definite integral

$-5\cdot 2-1\cdot -5\cdot 0$

Simplify the expression

$-10$
5

The integral $\int_{0}^{2}-5dx$ results in: $-10$

$-10$
6

Gather the results of all integrals

$\frac{32}{5}+\frac{16}{3}-10$

Simplify the addition $\frac{32}{5}+\frac{16}{3}-10$

$\frac{32-10\cdot 5}{5}+\frac{16}{3}$

Multiply $-10$ times $5$

$\frac{32-50}{5}+\frac{16}{3}$

Subtract the values $32$ and $-50$

$-\frac{18}{5}+\frac{16}{3}$
7

Simplify the addition $\frac{32}{5}+\frac{16}{3}-10$

$-\frac{18}{5}+\frac{16}{3}$

##  Final answer to the problem

$-\frac{18}{5}+\frac{16}{3}$

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