Homework Help is Here – Start Your Trial Now!
Math
Calculus
I guess those rectangles weren't so sudden. I was driving to a birthday party at my friend's house when I had the realization: I forgot the birthday gift. My velocity at t seconds after the realization is measured in meters per second and given by the function v(t) = 20 – 21, where traveling towards my friend's house is the positive direction. Label Equation/Value Displacement on [0,10] 100 Approx. Displace on [0,10] Displacement on [10,20] -100 As we saw on the previous slide, the area of these rectangles is connected with the approach we used to approximate displacement. Specifically, the base of the Oh nel The gh rend Hoe rectangles is given by the length of our intervals, or how often we "check" the velocity when we're doing our approximation. I've added a slider to the graph. See what happens as we make the base of our rectangles shorter, or we "check" the velocity more and more times. My house (2, 20) 10 You should see that the shaded area gets closer and closer to the area between the line (we'll call it a curve) and the x-axis. This is a big deal! Now, using the triangle area formula A = bh, find the area between the curve and the x-axis on the interval [0,10]. 20

I guess those rectangles weren't so sudden. I was driving to a birthday party at my friend's house when I had the realization: I forgot the birthday gift. My velocity at t seconds after the realization is measured in meters per second and given by the function v(t) = 20 – 21, where traveling towards my friend's house is the positive direction. Label Equation/Value Displacement on [0,10] 100 Approx. Displace on [0,10] Displacement on [10,20] -100 As we saw on the previous slide, the area of these rectangles is connected with the approach we used to approximate displacement. Specifically, the base of the Oh nel The gh rend Hoe rectangles is given by the length of our intervals, or how often we "check" the velocity when we're doing our approximation. I've added a slider to the graph. See what happens as we make the base of our rectangles shorter, or we "check" the velocity more and more times. My house (2, 20) 10 You should see that the shaded area gets closer and closer to the area between the line (we'll call it a curve) and the x-axis. This is a big deal! Now, using the triangle area formula A = bh, find the area between the curve and the x-axis on the interval [0,10]. 20

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
I guess those rectangles weren't so sudden.. I was driving to a birthday party at my friend's house when I had the realization: I forgot the birthday gift. My velocity at i seconds after the realization is measured in meters per second and given by the function v(t) = 20 – 2t, where traveling towards my friend's house is the positive direction. Label Equation/Value Displacement on [0,10] 100 Approx. Displace on [0,10] Displacement on [10,20] -100 As we saw on the previous slide, the area of these rectangles is connected with the approach we used to approximate displacement. Specifically, the base of the Oh nol The gtl Frends Houne rectangles is given by the length of our intervals, or how often we "check" the velocity when we're doing our approximation. I've added a slider to the graph. See what happens as we make the base of our rectangles shorter, or we "check" the velocity more and more times. My house |(2, 20) 20 10 You should see that the shaded area gets closer and closer to the area between the line (we'l call it a curve) and the x-axis. This is a big deal! Now, using the triangle area formula A = bh, find the area between the curve and the x-axis on the interval [0,10].
Transcribed Image Text:I guess those rectangles weren't so sudden.. I was driving to a birthday party at my friend's house when I had the realization: I forgot the birthday gift. My velocity at i seconds after the realization is measured in meters per second and given by the function v(t) = 20 – 2t, where traveling towards my friend's house is the positive direction. Label Equation/Value Displacement on [0,10] 100 Approx. Displace on [0,10] Displacement on [10,20] -100 As we saw on the previous slide, the area of these rectangles is connected with the approach we used to approximate displacement. Specifically, the base of the Oh nol The gtl Frends Houne rectangles is given by the length of our intervals, or how often we "check" the velocity when we're doing our approximation. I've added a slider to the graph. See what happens as we make the base of our rectangles shorter, or we "check" the velocity more and more times. My house |(2, 20) 20 10 You should see that the shaded area gets closer and closer to the area between the line (we'l call it a curve) and the x-axis. This is a big deal! Now, using the triangle area formula A = bh, find the area between the curve and the x-axis on the interval [0,10].
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Parabolas
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS