CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 14. Concepts of Calculus

14.9 Area Under a Curve http://www.ck12.org Contents

Here you will estimate the area under a curve and interpret its meaning in context.
Calculating the area under a straight line can be done with geometry. Calculating the area under a curved line
requires calculus. Often the area under a curve can be interpreted as the accumulated amount of whatever the
function is modeling. Suppose a car’s speed in meters per second can be modeled by a quadratic for the first 8
seconds of acceleration:
s(t) =t^2
How far has the car traveled in 8 seconds?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/62355

http://www.youtube.com/watch?v=Z_OHgubPJKA James Sousa: Interpret the Meaning of Area Under a Function

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/62357

http://www.youtube.com/watch?v=BvwyTXeuLS0 James Sousa: Approximate the Area Under a Curve with 4
Right Sided Rectangles

Guidance

The area under a curve can be approximated with rectangles equally spaced under a curve as shown below. For
consistency, you can choose whether the boxes should hit the curve on the left hand corner, the right hand corner,
the maximum value, or the minimum value. The more boxes you use the narrower the boxes will be and thus, the
more accurate your approximation of the area will be.