2.7.3 AP calculus Exam Riemann sum

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SUMMARY

The discussion focuses on calculating the Riemann sum for a given function R(t) over the interval from 4 to 15, using specific heights at defined points. The calculation includes the initial value of 50 liters and the sum of products of interval widths and corresponding heights, resulting in an approximate total of 114.9 liters. Participants clarify that the intervals do not need to be equal, which is crucial for accurate integration. Additionally, there is a query regarding the graphical representation of ticks on a graphing program.

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  • Familiarity with definite integrals and their computation.
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karush
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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.
 

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$\displaystyle 50 + \int_4^{15} R(t) \, dt \approx 50 + (3 \cdot 6.2 + 5 \cdot 5.9 + 3 \cdot 5.6) = 114.9 \text{ L}$
 

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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?
 
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)
 

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