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Find the most general antiderivative. S(-8 sec² x) dx -8 cot x + C 8 cot x + C tan x + C -8 tan x + C

Find the most general antiderivative. S(-8 sec² x) dx -8 cot x + C 8 cot x + C tan x + C -8 tan x + 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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**Question:** Find the most general antiderivative. \[ \int (-8 \sec^2 x) \, dx \] **Options:** - ( ) \(-8 \cot x + C\) - ( ) \(8 \cot x + C\) - ( ) \(\frac{\tan x}{8} + C\) - ( ) \(-8 \tan x + C\) In this problem, you're tasked with finding the antiderivative of \(-8 \sec^2 x\) with respect to \(x\). The antiderivative, also known as the indefinite integral, is a function that reverses the process of differentiation. The expression \(\int (-8 \sec^2 x) \, dx\) suggests using the basic antiderivative of \(\sec^2 x\), which is \(\tan x\), scaled by the constant \(-8\). Thus, the correct answer involves recognizing this relationship and applying the constant of integration \(C\).
Transcribed Image Text:**Question:** Find the most general antiderivative. \[ \int (-8 \sec^2 x) \, dx \] **Options:** - ( ) \(-8 \cot x + C\) - ( ) \(8 \cot x + C\) - ( ) \(\frac{\tan x}{8} + C\) - ( ) \(-8 \tan x + C\) In this problem, you're tasked with finding the antiderivative of \(-8 \sec^2 x\) with respect to \(x\). The antiderivative, also known as the indefinite integral, is a function that reverses the process of differentiation. The expression \(\int (-8 \sec^2 x) \, dx\) suggests using the basic antiderivative of \(\sec^2 x\), which is \(\tan x\), scaled by the constant \(-8\). Thus, the correct answer involves recognizing this relationship and applying the constant of integration \(C\).
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