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8 /12 - x² - 4x (A) (B C (D) dx = 16√12x² - 4x + C 2 sin ¹ (²+2) + C 8 sin ¹(²2) + C 8 sin ¹(+²) + C

8 /12 - x² - 4x (A) (B C (D) dx = 16√12x² - 4x + C 2 sin ¹ (²+2) + C 8 sin ¹(²2) + C 8 sin ¹(+²) + C

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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## Algebra Long Division ### Question 4 Evaluate the integral: \[ \int \frac{8}{\sqrt{12 - x^2 - 4x}} \, dx \] Choose the correct option: A) \( 16 \sqrt{12 - x^2 - 4x} + C \) B) \( 2 \sin^{-1} \left( \frac{x + 2}{4} \right) + C \) C) \( 8 \sin^{-1} \left( \frac{x - 2}{4} \right) + C \) D) \( 8 \sin^{-1} \left( \frac{x + 2}{4} \right) + C \) **Note:** Each option includes an arbitrary constant of integration \( C \).
Transcribed Image Text:## Algebra Long Division ### Question 4 Evaluate the integral: \[ \int \frac{8}{\sqrt{12 - x^2 - 4x}} \, dx \] Choose the correct option: A) \( 16 \sqrt{12 - x^2 - 4x} + C \) B) \( 2 \sin^{-1} \left( \frac{x + 2}{4} \right) + C \) C) \( 8 \sin^{-1} \left( \frac{x - 2}{4} \right) + C \) D) \( 8 \sin^{-1} \left( \frac{x + 2}{4} \right) + C \) **Note:** Each option includes an arbitrary constant of integration \( C \).
The image presents a calculus problem involving an integral, specifically: \[ \int \frac{8}{\sqrt{12 - x^2 - 4x}} \, dx = \] Four potential answers are provided, labeled A through D: **A)** \( 16\sqrt{12 - x^2 - 4x} + C \) **B)** \( 2 \sin^{-1} \left( \frac{x+2}{4} \right) + C \) **C)** \( 8 \sin^{-1} \left( \frac{x-2}{4} \right) + C \) **D)** \( 8 \sin^{-1} \left( \frac{x+2}{4} \right) + C \) Where \( C \) represents the constant of integration. The problem is to evaluate the integral and determine which of the given options is correct. Each option reflects a different expression based on the antiderivatives of the given function under the integral.
Transcribed Image Text:The image presents a calculus problem involving an integral, specifically: \[ \int \frac{8}{\sqrt{12 - x^2 - 4x}} \, dx = \] Four potential answers are provided, labeled A through D: **A)** \( 16\sqrt{12 - x^2 - 4x} + C \) **B)** \( 2 \sin^{-1} \left( \frac{x+2}{4} \right) + C \) **C)** \( 8 \sin^{-1} \left( \frac{x-2}{4} \right) + C \) **D)** \( 8 \sin^{-1} \left( \frac{x+2}{4} \right) + C \) Where \( C \) represents the constant of integration. The problem is to evaluate the integral and determine which of the given options is correct. Each option reflects a different expression based on the antiderivatives of the given function under the integral.
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