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AB5: Use a left Riemann sum with the three subintervals indicated by the table above to approximate SP P(t)dt.

AB5: Use a left Riemann sum with the three subintervals indicated by the table above to approximate SP P(t)dt.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### People Entering a School Over Time The table below represents the rate at which people enter a school over a period of 6 seconds. The variable \( t \) represents time in seconds, and \( P(t) \) represents the rate of people entering the school, measured in people per second. | \( t \) (seconds) | 0 | 1 | 4 | 6 | |----------------|---|---|---|---| | \( P(t) \) (people per second) | 8 | 3 | 5 | 10 | For \( 0 \leq t \leq 6 \) seconds, people enter a school at the rate \( P(t) \), measured in people per second. ### Explanation of the Table - At \( t = 0 \) seconds, the rate of people entering the school is 8 people per second. - At \( t = 1 \) second, the rate decreases to 3 people per second. - At \( t = 4 \) seconds, the rate increases slightly to 5 people per second. - At \( t = 6 \) seconds, the rate further increases to 10 people per second.
Transcribed Image Text:### People Entering a School Over Time The table below represents the rate at which people enter a school over a period of 6 seconds. The variable \( t \) represents time in seconds, and \( P(t) \) represents the rate of people entering the school, measured in people per second. | \( t \) (seconds) | 0 | 1 | 4 | 6 | |----------------|---|---|---|---| | \( P(t) \) (people per second) | 8 | 3 | 5 | 10 | For \( 0 \leq t \leq 6 \) seconds, people enter a school at the rate \( P(t) \), measured in people per second. ### Explanation of the Table - At \( t = 0 \) seconds, the rate of people entering the school is 8 people per second. - At \( t = 1 \) second, the rate decreases to 3 people per second. - At \( t = 4 \) seconds, the rate increases slightly to 5 people per second. - At \( t = 6 \) seconds, the rate further increases to 10 people per second.
### AB5: Approximate the Integral Using a Left Riemann Sum To approximate the integral \[ \int_{0}^{6} P(t) \, dt \] use a left Riemann sum with the three subintervals indicated by the table above.
Transcribed Image Text:### AB5: Approximate the Integral Using a Left Riemann Sum To approximate the integral \[ \int_{0}^{6} P(t) \, dt \] use a left Riemann sum with the three subintervals indicated by the table above.
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