Suppose you are driving away from Morgantown. At noon, you are 75 miles away from Morgantown. From noon until 5:00 pm, at any time t hours after noon, your velocity (miles per hour) is given by the function v(t) = -5t4 +50t3 - 163t² + 190t. 60 Left-Hand Sum: Right-Hand Sum: 50 40 30 20 10 0 Now, create a table of function values and use it to calculate the left and right hand sum. Put those values here. 2 If necessary, round to two decimal places. If necessary, round to two decimal places. Give this estimate here. 4 ... We will assume that using only four rectangles, the best estimate of the integral is half way in between the two sums, or the average of the two sums. S(-514 +501³ - 1631² + 190t) dt ≈ [ 0 If necessary, round to two decimal places.
Suppose you are driving away from Morgantown. At noon, you are 75 miles away from Morgantown. From noon until 5:00 pm, at any time t hours after noon, your velocity (miles per hour) is given by the function v(t) = -5t4 +50t3 - 163t² + 190t. 60 Left-Hand Sum: Right-Hand Sum: 50 40 30 20 10 0 Now, create a table of function values and use it to calculate the left and right hand sum. Put those values here. 2 If necessary, round to two decimal places. If necessary, round to two decimal places. Give this estimate here. 4 ... We will assume that using only four rectangles, the best estimate of the integral is half way in between the two sums, or the average of the two sums. S(-514 +501³ - 1631² + 190t) dt ≈ [ 0 If necessary, round to two decimal places.
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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![### Calculating Distances Using Integration
#### Problem Description
Suppose you are driving away from Morgantown. At noon, you are 75 miles away from Morgantown. From noon until 5:00 pm, at any time \( t \) hours after noon, your velocity (miles per hour) is given by the function \( v(t) = -5t^4 + 50t^3 - 163t^2 + 190t \).
#### Graph Explanation
The provided graph displays the velocity function \( v(t) \) against time \( t \) in hours:
- **X-axis (horizontal)**: Represents time \( t \) from 0 to 4 hours.
- **Y-axis (vertical)**: Represents velocity \( v(t) \) in miles per hour from 0 to 60.
#### Task
Create a table of function values and use it to calculate the left-hand and right-hand sums. Input those values in the fields provided.
- **Left-Hand Sum: [______]** _(If necessary, round to two decimal places.)_
- **Right-Hand Sum: [______]** _(If necessary, round to two decimal places.)_
We assume that using only four rectangles, the best estimate of the integral is halfway between the two sums, or the average of the two sums.
#### Estimate Calculation
Give this estimate here:
\[
\int_{0}^{4} (-5t^4 + 50t^3 - 163t^2 + 190t) \, dt \approx \left[ \text{Average of Left-Hand and Right-Hand Sums} \right]
\]
- **Estimate: [______]** _(If necessary, round to two decimal places.)_
By integrating the velocity function \( v(t) \) you can determine the total distance traveled during the given time interval. This can be approached by numerical integration methods such as left-hand and right-hand sums with rectangle approximations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd379b166-bb3f-49cc-8f67-a1e231fb014b%2Fb773716d-2cda-466e-9b63-f69e330065d3%2Fpe1ezzg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Distances Using Integration
#### Problem Description
Suppose you are driving away from Morgantown. At noon, you are 75 miles away from Morgantown. From noon until 5:00 pm, at any time \( t \) hours after noon, your velocity (miles per hour) is given by the function \( v(t) = -5t^4 + 50t^3 - 163t^2 + 190t \).
#### Graph Explanation
The provided graph displays the velocity function \( v(t) \) against time \( t \) in hours:
- **X-axis (horizontal)**: Represents time \( t \) from 0 to 4 hours.
- **Y-axis (vertical)**: Represents velocity \( v(t) \) in miles per hour from 0 to 60.
#### Task
Create a table of function values and use it to calculate the left-hand and right-hand sums. Input those values in the fields provided.
- **Left-Hand Sum: [______]** _(If necessary, round to two decimal places.)_
- **Right-Hand Sum: [______]** _(If necessary, round to two decimal places.)_
We assume that using only four rectangles, the best estimate of the integral is halfway between the two sums, or the average of the two sums.
#### Estimate Calculation
Give this estimate here:
\[
\int_{0}^{4} (-5t^4 + 50t^3 - 163t^2 + 190t) \, dt \approx \left[ \text{Average of Left-Hand and Right-Hand Sums} \right]
\]
- **Estimate: [______]** _(If necessary, round to two decimal places.)_
By integrating the velocity function \( v(t) \) you can determine the total distance traveled during the given time interval. This can be approached by numerical integration methods such as left-hand and right-hand sums with rectangle approximations.
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