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.

Symbolic mode

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

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

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

$\int_<0>^ x^4dx+\int_<0>^2x^2dx+\int_<0>^-5dx$

 Intermediate steps

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

$\left[\frac>\right]_^$Evaluate the definite integral

The integral $\int_^ x^4dx$ results in: $\frac$

 Explain this step further

 Intermediate steps

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

$2\int_<0>^ x^2dx$

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

$2\left[\frac>\right]_^$Evaluate the definite integral

$2\cdot \left(\frac>- \frac<0^>\right)$Simplify the expression

The integral $\int_^2x^2dx$ results in: $\frac$

 Explain this step further

 Intermediate steps

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

$\left[-5x\right]_<0>^$

Evaluate the definite integral

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

The integral $\int_^-5dx$ results in: $-10$

 Explain this step further

Gather the results of all integrals

$\frac<32>+\frac-10$

 Intermediate steps

Simplify the addition $\frac+\frac-10$

Multiply $-10$ times $5$

Subtract the values $32$ and $-50$

Simplify the addition $\frac+\frac-10$