Using rectangles to approximate area under a curve

The  exercise appears under the Integral calculus Math Mission. This exercise uses rectangles to approximate the area under a curve.

Types of Problems
There is one type of problem in this exercise:


 * 1) Represent the integral as rectangle area: This problem presents a graph with several sketched on rectangles. The student is expected to select the option that represents the sum of the rectangles in the diagram.Urtaauac1.png

Strategies
Knowledge of geometric area formulas and the concept of integration as area under the curve are encouraged to ensure success on this exercise.
 * 1) When the sigma notation is provided, plugging in the first bound of the sigma should be the area of one of the rectangles, the furthest left.
 * 2) The number of rectangles can be counted by the bounds on the sigma notation.

Real-life Applications

 * 1) Geometrically an integral can be used to find area and volume formulas.
 * 2) The use of rectangles to approximate area is useful in math classes like numerical analysis.
 * 3) Approximation methods, such as the rectangle sum, can be used to find integrals for which no closed-form antiderivative exists.