- t+t² g(x) = √3x +z-t dt 1

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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Use FTC1 to find the derivative

The image shows a mathematical expression for the function \( g(x) \) defined as an integral:

\[ g(x) = \int_{1}^{3x} \frac{t + t^2}{2 - t} \, dt \]

Explanation:

- The function \( g(x) \) is represented as a definite integral.
- The limits of integration are from 1 to \( 3x \).
- The integrand is the expression \(\frac{t + t^2}{2 - t}\).
- The integration variable is \( t \). 

This integral represents an area under the curve defined by the integrand \(\frac{t + t^2}{2 - t}\) between the limits 1 and \(3x\).
Transcribed Image Text:The image shows a mathematical expression for the function \( g(x) \) defined as an integral: \[ g(x) = \int_{1}^{3x} \frac{t + t^2}{2 - t} \, dt \] Explanation: - The function \( g(x) \) is represented as a definite integral. - The limits of integration are from 1 to \( 3x \). - The integrand is the expression \(\frac{t + t^2}{2 - t}\). - The integration variable is \( t \). This integral represents an area under the curve defined by the integrand \(\frac{t + t^2}{2 - t}\) between the limits 1 and \(3x\).
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