# How do you find the area under a curve using integrals?

Sep 3, 2014

Finding the area under a curve is easy use and integral is pretty simple. First you take the indefinite that solve it using your higher and lower bounds. Lastly you subtract the answer from the higher bound from the lower bound.

For example, lets take the function,

$f \left(x\right) = x$

and we want to know the area under it between the points where
$x = 0$ and $x = 5$.

First you set up your integral ${\int}_{0}^{5} x \mathrm{dx}$.

Next you find the indefinite integral.

$\int x \mathrm{dx} = \frac{1}{2} \cdot {x}^{2} + C$

Now you plugin the 5 and the 0 and solve

$\left(\frac{1}{2} \cdot {5}^{2} + C\right) - \left(\frac{1}{2} \cdot {0}^{2} + C\right) = 12.5$

Because this example forms a triangle, we can check the answer with the equation for the area

$A = \frac{1}{2} \cdot 5 \cdot 5 = 12.5$