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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![The expression in the image is the integral:
\[
\int 3x^2 (x^3 - 5)^7 \, dx
\]
This represents an indefinite integral, which is used in calculus to find the antiderivative of the function \(3x^2 (x^3 - 5)^7\) with respect to \(x\).
Key components:
- \(3x^2\) is the leading term outside the parentheses.
- \( (x^3 - 5)^7 \) represents a polynomial expression raised to the seventh power.
- \(dx\) indicates that the integration is with respect to the variable \(x\).
To solve this integral, techniques such as substitution may be used, whereby \(u = x^3 - 5\) and \(du = 3x^2 dx\), simplifying the integration process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e8eaad3-4d91-4777-be35-ba41f897f0fa%2F50917afc-1387-4f48-baca-ec510de142ec%2Fgyyugwm_processed.png&w=3840&q=75)
Transcribed Image Text:The expression in the image is the integral:
\[
\int 3x^2 (x^3 - 5)^7 \, dx
\]
This represents an indefinite integral, which is used in calculus to find the antiderivative of the function \(3x^2 (x^3 - 5)^7\) with respect to \(x\).
Key components:
- \(3x^2\) is the leading term outside the parentheses.
- \( (x^3 - 5)^7 \) represents a polynomial expression raised to the seventh power.
- \(dx\) indicates that the integration is with respect to the variable \(x\).
To solve this integral, techniques such as substitution may be used, whereby \(u = x^3 - 5\) and \(du = 3x^2 dx\), simplifying the integration process.
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