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 \( x = 3 \).

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Answered: y = x? - x - 12, y = 0, x = -3, x = 3 y…

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.

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...

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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 \( x = 3 \).

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