Homework Help is Here – Start Your Trial Now!
Math
Calculus
y = x? - x - 12, y = 0, x = -3, x = 3 y 10 10 10 10 5 -4 2 -4 -2 4 2 4 -5 - 10 10 -10 -10 Find the area of the region.

y = x? - x - 12, y = 0, x = -3, x = 3 y 10 10 10 10 5 -4 2 -4 -2 4 2 4 -5 - 10 10 -10 -10 Find the area of the region.

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

Sketch the region bounded by the graphs of the functions.

y = x2 − x − 12, y = 0, x = −3, x = 3

The image presents four graphs of quadratic functions, illustrating the calculation of areas for shaded regions under the curve. The function given is \( y = x^2 - x - 12 \), with constraints \( y = 0 \), \( x = -3 \), and \( x = 3 \). The task is to find the area of the shaded region among the options. **Graph Details:** 1. **First Graph:** - A downward-opening parabola with the area above the x-axis shaded in blue between \( x = -3 \) and \( x = 3 \). 2. **Second Graph:** - An upward-opening parabola with the area below the x-axis shaded in blue between the same x values. 3. **Third Graph:** - Another downward-opening parabola similar to the first graph, but the shaded area is below the x-axis. 4. **Fourth Graph:** - A downward-opening parabola with the area above the x-axis shaded, indicating the region being enclosed between \( x = -3 \) and \( x = 3 \). The problem asks to identify which shaded region correctly represents the bounded area for integration. The correct area is suggested by the fourth option, which is highlighted. The task is to compute the area and input it in the provided space. Instructions on solving areas under curves typically involve integrating the given quadratic function over the specified limits \( x = -3 \) and \( x = 3 \).
Transcribed Image Text:The image presents four graphs of quadratic functions, illustrating the calculation of areas for shaded regions under the curve. The function given is \( y = x^2 - x - 12 \), with constraints \( y = 0 \), \( x = -3 \), and \( x = 3 \). The task is to find the area of the shaded region among the options. **Graph Details:** 1. **First Graph:** - A downward-opening parabola with the area above the x-axis shaded in blue between \( x = -3 \) and \( x = 3 \). 2. **Second Graph:** - An upward-opening parabola with the area below the x-axis shaded in blue between the same x values. 3. **Third Graph:** - Another downward-opening parabola similar to the first graph, but the shaded area is below the x-axis. 4. **Fourth Graph:** - A downward-opening parabola with the area above the x-axis shaded, indicating the region being enclosed between \( x = -3 \) and \( x = 3 \). The problem asks to identify which shaded region correctly represents the bounded area for integration. The correct area is suggested by the fourth option, which is highlighted. The task is to compute the area and input it in the provided space. Instructions on solving areas under curves typically involve integrating the given quadratic function over the specified limits \( x = -3 \) and \( x = 3 \).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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