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Evaluate the integral fx² cos(4- x³) dx sin(4 — x³)+C O -sin

Evaluate the integral fx² cos(4- x³) dx sin(4 — x³)+C O -sin

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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**Problem Statement:** Evaluate the integral \(\int x^2 \cos(4 - x^3) \, dx\). **Options:** 1. \(\large\textcolor{blue}{\bullet}\) \(-\frac{1}{3}\sin(4 - x^3) + C\) 2. \(\circ\) \(-\frac{1}{3}\cos(4 - x^3) + C\) 3. \(\circ\) \(\frac{1}{3}\sin(4 - x^3) + C\) 4. \(\circ\) \(\frac{1}{3}\sin(4 - x^2) + C\) **Explanation:** The problem requires finding the integral of a function involving trigonometric expressions. The integral is evaluated with respect to \(x\) and includes \(x^2\) multiplied by the cosine of a cubic expression \((4 - x^3)\). The correct answer to this integral is choice 1: \(-\frac{1}{3}\sin(4 - x^3) + C\), where \(C\) represents the constant of integration.
Transcribed Image Text:**Problem Statement:** Evaluate the integral \(\int x^2 \cos(4 - x^3) \, dx\). **Options:** 1. \(\large\textcolor{blue}{\bullet}\) \(-\frac{1}{3}\sin(4 - x^3) + C\) 2. \(\circ\) \(-\frac{1}{3}\cos(4 - x^3) + C\) 3. \(\circ\) \(\frac{1}{3}\sin(4 - x^3) + C\) 4. \(\circ\) \(\frac{1}{3}\sin(4 - x^2) + C\) **Explanation:** The problem requires finding the integral of a function involving trigonometric expressions. The integral is evaluated with respect to \(x\) and includes \(x^2\) multiplied by the cosine of a cubic expression \((4 - x^3)\). The correct answer to this integral is choice 1: \(-\frac{1}{3}\sin(4 - x^3) + C\), where \(C\) represents the constant of integration.
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