# How do you evaluate the definite integral #int(5x^(1/3))dx# from #[-2,2]#?

##### 1 Answer

#### Explanation:

We have that:

where the limits applied to integral come from the interval you have been asked to evaluate. To begin simply integrate the function:

Now evaluate by simply substituting in the limits like so:

It is also possible to arrive at this result intuitively by exploiting the symmetry of the function.

That is, the function has odd symmetry. If we plot this function we can see clearly that the function is reflected but negative through the y -axis. As a result, over the interval the area above the x-axis will exactly cancel with the area under the x-axis giving us

graph{5x^(1/3) [-18.19, 18.19, -9.1, 9.09]}