Question

What is `int_(0)^(2) x^(3)dx`?

Answer 1

4 sq units

Explanation:

Remember that an application of integration is to find the area under a curve. In this example you are finding the area bounded between 0 and 2.

First you apply the integration rules.

`int x^3dx=(x^4)/4`

Now apply the bounds of 0 and 2.

`[(x^4)/4]_0^2`

Substitute in the upper bound into the expression
Substitute in the lower bound into the expression
Subtract the lower bound result from the upper bound result

`[(x^4)/4]_0^2=(2^4)/4-(0^4)/4=16/4-0=16/4=4` square units