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Calculate the following integral: 4 I V16 - x dx .2 0.

Calculate the following integral: 4 I V16 - x dx .2 0.

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
**Calculate the following integral:** \[ \int_{0}^{4} \sqrt{16 - x^2} \, dx \] This integral represents the area under the curve of the function \(\sqrt{16 - x^2}\) from \(x = 0\) to \(x = 4\). The expression under the square root, \(16 - x^2\), is characteristic of a semicircle's equation when rearranged as \(x^2 + y^2 = 16\). Here, the integral calculates one quadrant of this circle, specifically over the interval provided.
Transcribed Image Text:**Calculate the following integral:** \[ \int_{0}^{4} \sqrt{16 - x^2} \, dx \] This integral represents the area under the curve of the function \(\sqrt{16 - x^2}\) from \(x = 0\) to \(x = 4\). The expression under the square root, \(16 - x^2\), is characteristic of a semicircle's equation when rearranged as \(x^2 + y^2 = 16\). Here, the integral calculates one quadrant of this circle, specifically over the interval provided.
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