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Use integration techniques to find the area of the region enclosed between the curve y = v4– and the r-axis.

Use integration techniques to find the area of the region enclosed between the curve y = v4– and the r-axis.

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...
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Question
**5. Use integration techniques to find the area of the region enclosed between the curve \( y = \sqrt{4 - x^2} \) and the x-axis.** To find the area of the region enclosed by the curve and the x-axis, you will need to: 1. Set up the definite integral, as the area will be the integral of the function \( \sqrt{4 - x^2} \) from its starting point to its ending point on the x-axis. 2. Determine the interval of integration by finding the x-intercepts of the function. 3. Evaluate the definite integral to find the area.
Transcribed Image Text:**5. Use integration techniques to find the area of the region enclosed between the curve \( y = \sqrt{4 - x^2} \) and the x-axis.** To find the area of the region enclosed by the curve and the x-axis, you will need to: 1. Set up the definite integral, as the area will be the integral of the function \( \sqrt{4 - x^2} \) from its starting point to its ending point on the x-axis. 2. Determine the interval of integration by finding the x-intercepts of the function. 3. Evaluate the definite integral to find the area.
Expert Solution
Step 1

We first sketch the region using a graphing calculator 

Calculus homework question answer, step 1, image 1

x is from -2 to 2 (from the graph)

 

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