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Integrate the function. .2 x- 16 dx X 2 - 16 O A. sec + C 16 OB. An -16 - () c B. 4 In Vx - 16 +C x² - 16 .2 C. 4 + C sec 4

Integrate the function. .2 x- 16 dx X 2 - 16 O A. sec + C 16 OB. An -16 - () c B. 4 In Vx - 16 +C x² - 16 .2 C. 4 + C sec 4

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
**Problem: Integrate the function.** \[ \int \frac{\sqrt{x^2 - 16}}{x} \, dx \] **Options:** - **A.** \[ \left[ \frac{\sqrt{x^2 - 16}}{16} - \sec^{-1}\left(\frac{x}{4}\right) \right] + C \] - **B.** \[ 4 \ln \left| \sqrt{x^2 - 16} - \left(\frac{x}{4}\right) \right| + C \] - **C.** \[ 4 \left[ \frac{\sqrt{x^2 - 16}}{4} - \sec^{-1}\left(\frac{x}{4}\right) \right] + C \] - **D.** \[ 4 \left[ \frac{\sqrt{x^2 - 16}}{4} - \sin^{-1}\left(\frac{x}{4}\right) \right] + C \] **Explanation of options:** Each option provides a different solution form involving integrals with inverse trigonometric functions and logarithms, where \( C \) represents the constant of integration. Options C and D use the expression in brackets with inverse secant or inverse sine functions, respectively.
Transcribed Image Text:**Problem: Integrate the function.** \[ \int \frac{\sqrt{x^2 - 16}}{x} \, dx \] **Options:** - **A.** \[ \left[ \frac{\sqrt{x^2 - 16}}{16} - \sec^{-1}\left(\frac{x}{4}\right) \right] + C \] - **B.** \[ 4 \ln \left| \sqrt{x^2 - 16} - \left(\frac{x}{4}\right) \right| + C \] - **C.** \[ 4 \left[ \frac{\sqrt{x^2 - 16}}{4} - \sec^{-1}\left(\frac{x}{4}\right) \right] + C \] - **D.** \[ 4 \left[ \frac{\sqrt{x^2 - 16}}{4} - \sin^{-1}\left(\frac{x}{4}\right) \right] + C \] **Explanation of options:** Each option provides a different solution form involving integrals with inverse trigonometric functions and logarithms, where \( C \) represents the constant of integration. Options C and D use the expression in brackets with inverse secant or inverse sine functions, respectively.
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