Investigating Integrals through Polygons

This applet will allow you to visually observe how an integral can approximate the area under a curve. The concept is to see that as the distance between the two parallel lines becomes smaller so does the inaccuracy fo the approximation of that section under the curve. Please enter the corresponding left and right distances so you can see how the areas relate.

Instructions:
1: Drag the right and left constraint slider to your desired location. Keep the left constraint on the left and the right respectively.
2: Enter the value of the left constraint (a) into t[0].
3: Enter the value of the right constraint (b) into t[1].
4: Observe how the approximate area and the definite integral area relate.

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left constraint (a)
0 0 24.218407
right constraint (b)
0 0 44.658213
t[0]
t[1]
a
aprx_area
b
int_area

This visual will help you understand the concept of a Reiman Sum for approximating the area under a curve. With smaller and more rectangles or trapezoids, an area approximation becomes closer to the definite integra calculated. It makes sense that no matter how small the Reiman sum trapezoid is, the approximate area will always be smaller because of the area lost between the curve and itself.

App generated by Geometry Expressions