Practice Integral in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The reverse operation of differentiation; it also computes the exact area under a curve between two points.

If derivative gives rate, integral gives total. Derivative of position = velocity; integral of velocity = position.

Example 1

easy
Find \int (4x^3 + 6x) \, dx

Example 2

medium
Evaluate \int_0^2 (3x^2 + 1) \, dx

Example 3

easy
Find \int (5x^2 - 3x + 7) \, dx

Example 4

hard
Find \int \frac{1}{x} \, dx and explain why the standard power rule does not apply.