The graph of a function f ( x ) is given below. (Each grid square is 1 unit wide
ID: 2878800 • Letter: T
Question
The graph of a function f(x) is given below. (Each grid square is 1 unit wide and 1 unit high.)
Use rectangles to estimate the area under the curve on the interval. (Determine the number of rectangles, the width of the rectangles in each case, and which sample points should be used in your calculation using the given directions. When determining the height of a rectangle, assume that the height is a multiple of 0.5.)
a.) On the interval [0, 12] using 4 subintervals of equal width and right endpoints as sample points.
_________square units
(b) On the interval [0, 12] using 12 subintervals of equal width and right endpoints as sample points.
_______ square units
(c) On the interval [0, 12] using 6 subintervals of equal width and midpoints as sample points.
________ square units
Explanation / Answer
a.
On the interval [0, 12] using 4 subintervals there will be total 4 rectangles thus
the area under the curve on the interval = 1*2 +3*3+2*3+2*3= 23 square unit
b.
On the interval [0, 12] using 12 subintervals
the area under the curve on the interval = 1+2+3+3+3+2+2+2+2+3+4 = 27 square unit
c.
On the interval [0, 12] using 12 subintervals
the area under the curve on the interval = 1+4+6+4+4+6 = 25 square unit
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.