c. Find the area of the shaded region constructed in part b by using a common geometric area formula. d. Find the area of the shaded region constructed in part b by evaluating the definite integral from part a. (Hint: Areas from parts c and d should match) 2. Let's assume now that the acceleration of the car is not a constant positive value, but one that is constantly increasing as well. After all, you don't want to floor the gas pedal from rest, but gradually want to push it down to the floorboard as the car is moving 11 over time. Therefore, the velocity function to consider now is v(t) = =t², which 8. satisfies both the car starting at rest (0,0) and moving at 88 ft/sec after 8 seconds (8,88). a. Write the definite integral for this journey with Dr. Lawrence's Impala. What type of measurement would be produced when evaluating this definite integral? b. Trace the graph of v(t) on the graph below and shade the area underneath v(t) bounded by the proper interval. Label the axes appropriately. Since a common geometric area formula will not be useful here as there exists a nonlinear side, use left Riemann Sums with four subintervals to find an approximation of the area sketched in part b. 2° d. Use right Riemann Sums with four subintervals to find an approximation of the area sketched in part b. 2- e. Find the exact area of the shaded region constructed in part b by evaluating the definite integral from part a.
c. Find the area of the shaded region constructed in part b by using a common geometric area formula. d. Find the area of the shaded region constructed in part b by evaluating the definite integral from part a. (Hint: Areas from parts c and d should match) 2. Let's assume now that the acceleration of the car is not a constant positive value, but one that is constantly increasing as well. After all, you don't want to floor the gas pedal from rest, but gradually want to push it down to the floorboard as the car is moving 11 over time. Therefore, the velocity function to consider now is v(t) = =t², which 8. satisfies both the car starting at rest (0,0) and moving at 88 ft/sec after 8 seconds (8,88). a. Write the definite integral for this journey with Dr. Lawrence's Impala. What type of measurement would be produced when evaluating this definite integral? b. Trace the graph of v(t) on the graph below and shade the area underneath v(t) bounded by the proper interval. Label the axes appropriately. Since a common geometric area formula will not be useful here as there exists a nonlinear side, use left Riemann Sums with four subintervals to find an approximation of the area sketched in part b. 2° d. Use right Riemann Sums with four subintervals to find an approximation of the area sketched in part b. 2- e. Find the exact area of the shaded region constructed in part b by evaluating the definite integral from part a.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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can you help with 2C it's circled in PINK on the top of the second page, i am in high school struggling with this.
Transcribed Image Text:c. Find the area of the shaded region constructed in part b by using a common
geometric area formula.
d. Find the area of the shaded region constructed in part b by evaluating the definite
integral from part a. (Hint: Areas from parts c and d should match)
2. Let's assume now that the acceleration of the car is not a constant positive value, but
one that is constantly increasing as well. After all, you don't want to floor the gas pedal
from rest, but gradually want to push it down to the floorboard as the car is moving
11
over time. Therefore, the velocity function to consider now is v(t) = =t², which
8.
satisfies both the car starting at rest (0,0) and moving at 88 ft/sec after 8 seconds (8,88).
a. Write the definite integral for this journey with Dr. Lawrence's Impala. What
type of measurement would be produced when evaluating this definite integral?
b. Trace the graph of v(t) on the graph below and shade the area underneath v(t)
bounded by the proper interval. Label the axes appropriately.
Transcribed Image Text:Since a common geometric area formula will not be useful here as there exists a
nonlinear side, use left Riemann Sums with four subintervals to find an
approximation of the area sketched in part b.
2°
d. Use right Riemann Sums with four subintervals to find an approximation of the
area sketched in part b.
2-
e. Find the exact area of the shaded region constructed in part b by evaluating the
definite integral from part a.
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