The Area between a curve and an axis exercise appears under the Integral calculus Math Mission on Khan Academy. This exercise shows how to evaluate the antiderivative in respect to the curve and the axis.

Types of Problems Edit

Area Between curve and axis

Find the area of function given the function and graph

There are two types of problems in this exercise:

  1. Find the zeros of the function: The student is asked to find the zeros of the function given the graph and equation.
  2. Find the area of the shaded region: The student is asked to find the area of the shaded region on a particular axis or quadrant. 

Strategies Edit

Knowledge of Riemann sums and the fundamental theorem of calculus are encouraged to ensure success on this exercise.

  1. The area between a curve and an axis is the antiderivative of the upper bound of the function minis the antiderivative of the lower bound of the function.
  2. Students can find the zeros of a function by using synthetic division. 
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