2.7.3 AP calculus Exam Riemann sum

In summary, the conversation discusses the intervals of time in which a certain function is applied, and how it relates to calculating a total amount. The speaker also brings up the possibility of showing only relevant data on a graph.
  • #1
karush
Gold Member
MHB
3,269
5
View attachment 9364

ok basically t is 3 hours appart except between 7 and 12 of which I didn't know if we should intemperate.
other wise it is just adding up the 4 $(t)\cdot(R(t))$s.
 

Attachments

  • 321.png
    321.png
    10.8 KB · Views: 85
Last edited:
Physics news on Phys.org
  • #2
$\displaystyle 50 + \int_4^{15} R(t) \, dt \approx 50 + (3 \cdot 6.2 + 5 \cdot 5.9 + 3 \cdot 5.6) = 114.9 \text{ L}$
 

Attachments

  • Right_sum.jpg
    Right_sum.jpg
    33.1 KB · Views: 77
  • #3
skeeter said:
$\displaystyle 50 + \int_4^{15} R(t) \, dt \approx 50 + (3 \cdot 6.2 + 5 \cdot 5.9 + 3 \cdot 5.6) = 114.9 \text{ L}$

ok, well I thot the intervals had to be equal but just take what is given here!

on your graph program is it possible just to show the ticks that apply?
 
  • #4
karush said:
ok, well I thot the intervals had to be equal but just take what is given here!

on your graph program is it possible just to show the ticks that apply?

the intervals do not have to be equal ... what do you mean by "ticks that apply" ?

first base [4,7], height is R(7)

second base [7,12], height is R(12)

last base [12,15], height is R(15)
 

FAQ: 2.7.3 AP calculus Exam Riemann sum

1. What is a Riemann sum in AP Calculus?

A Riemann sum is a method used in calculus to approximate the area under a curve by dividing it into smaller rectangles and adding up their areas. It is an important concept in AP Calculus as it is used to find the exact value of integrals.

2. How is a Riemann sum calculated?

To calculate a Riemann sum, the interval of the curve is divided into n smaller intervals, and the width of each interval is determined. Then, the function is evaluated at a specific point within each interval, and the product of the width and the function value is added up for all the intervals to find the approximate area under the curve.

3. What is the significance of Riemann sum in AP Calculus?

Riemann sum is significant in AP Calculus as it is used to approximate the area under a curve and find the exact value of integrals. It is also used to determine the convergence or divergence of infinite series and to calculate the volume of irregularly shaped objects.

4. What are the different types of Riemann sums?

The three types of Riemann sums are left Riemann sum, right Riemann sum, and midpoint Riemann sum. In left Riemann sum, the function is evaluated at the left endpoint of each interval, while in right Riemann sum, the function is evaluated at the right endpoint of each interval. In midpoint Riemann sum, the function is evaluated at the midpoint of each interval.

5. How does Riemann sum relate to the definite integral?

Riemann sum is closely related to the definite integral as the definite integral is defined as the limit of Riemann sums as the number of intervals approaches infinity. In other words, the definite integral is the exact value of the area under a curve, while Riemann sum is an approximation of this value.

Similar threads

Replies
6
Views
2K
Replies
6
Views
2K
Replies
16
Views
3K
Replies
4
Views
2K
Replies
3
Views
1K
Replies
2
Views
2K
Replies
1
Views
1K
Replies
3
Views
1K
Back
Top