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# Integral Calculator

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Integral of a function is the antiderivative of that function and is called as indefinite integral. Basically, it is integrating the function with respect to its variable.

If g(x) is the function, then the indefinite integral is expressed as $\int g(x)$. You can see that the derivative of $\int g(x)$ is g(x).

This online Integral calculator will integrate tge given function with respect to the given variable.

## Steps

Step 1: Check the given function in the problem with its variable.

Step 2: Integrate the given function with respect to its variable and find the integrated value of the function.

## Problems

Below are some of the solved problems given based on integral.

### Solved Examples

Question 1: Evaluate the following function:
$g(x) = 5x^4 - 16x^2 + 8x dx$.
Solution:

Step 1: Given : $g(x) = 5x^4 - 16x^2 + 8x dx$

Step 2: $\int 5x^4 - 16x^2 + 8x dx$
= $5\int x^4 dx - 16\int x^2 dx + 8\int x dx$

= $\frac{5x^{5}}{5}$ - $\frac{16x^3}{3}$ + $\frac{8x^2}{2}$

= $x^{5}$ - $\frac{16x^3}{3}$ + 4$x^2$ + C

Therefore, $\int 5x^4 - 16x^2 + 8x dx$ = $x^{5}$ - $\frac{16x^3}{3}$ + 4$x^2$ + C

Question 2: Evaluate the following function:
$g(x) = 2sin(x)$.
Solution:

Step 1: Given : $g(x) = 2sin(x)$

Step 2: $\int 2sin(x)$
= $2 \int sin(x)$
= $-2cos(x)$

Therefore, $\int 2sin(x)$ = $-2cos(x)$