http://www.ck12.org Chapter 14. Concepts of Calculus
Concept Problem Revisited
You can use the area under the curve to find the total distance traveled in the first 8 seconds. Since the quadratic is a
curve you must choose the number of subintervals you want to use and whether you want right or left handed boxes
for estimating. Suppose you choose 8 left handed boxes of width one.
TABLE14.15:
x 0 1 2 3 4 5 6 7
Area of
box to the
right1 · 0 1 · 1 1 · 4 1 · 9 1 · 16 1 · 25 1 · 36 1 · 49
The approximate sum is 1+ 4 + 9 + 16 + 25 + 36 + 49 =140. This means that the car traveled approximately 140
meters in the first 8 seconds.
Vocabulary
Subintervalsare created when an interval is broken into smaller equally sized intervals.
Anintegralis the limit of a sum as the number of summands increases to infinity.
Using boxes to estimate the area under a curve is called aRiemann Sum.
Asummandis one of many pieces being summed together.
Guided Practice
- Approximate the area under the curve using eight subintervals and right endpoints.
f(x) = 3 x^2 − 1 ,− 1 ≤x≤ 7 - Approximate the area under the curve using eight subintervals and left endpoints.
f(x) =^4 x+ 3 , 2 ≤x≤ 6 - Approximate the area under the curve using twenty subintervals and left endpoints.
f(x) =xx, 1 ≤x≤ 3
Answers: