Calculus · Grades 11 to 12
Integrals
Reverse derivatives and measure area.
The idea
An antiderivative reverses a derivative. The power rule for integrals adds one to the power and divides by the new power.
A definite integral measures the area between the graph and the x-axis. Evaluate the antiderivative at the top limit, then subtract its value at the bottom limit.
Worked examples
- How to Find an Antiderivative Find the antiderivative of 3x^2. Three steps with the power rule for integrals, the constant C, and the mistakes to avoid.
- How to Evaluate a Definite Integral Evaluate the integral of 2x from 1 to 3. Four steps, the antiderivative, and the subtraction-order mistakes to avoid.
- How to Find a Limit by Factoring Evaluate the limit of (x^2 - 9)/(x - 3) as x goes to 3. Four steps, the 0/0 case, and the cancel mistakes to avoid.
Practice this topic
3 problems with answers.