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 equation presented is:
\[ c) \, g(x) = \int_{-\sqrt{x}}^{x} \frac{t}{\sqrt[3]{1 + t^2}} \, dt \]
This equation represents a definite integral of the function \(\frac{t}{\sqrt[3]{1 + t^2}}\) with respect to \(t\), evaluated from the lower limit \(-\sqrt{x}\) to the upper limit \(x\).
In this context:
- \(g(x)\) is the integral function of \(x\).
- The numerator \(t\) signifies the variable of integration.
- The denominator is the cube root of \(1 + t^2\), which affects the rate of change of the integrand within the integral's bounds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faea7a391-77a2-4be9-b3a3-98e0f70bf810%2Fa5a42fb3-b776-4099-b5da-d911e3aec098%2Fxs0r6cf_processed.png&w=3840&q=75)
Transcribed Image Text:The equation presented is:
\[ c) \, g(x) = \int_{-\sqrt{x}}^{x} \frac{t}{\sqrt[3]{1 + t^2}} \, dt \]
This equation represents a definite integral of the function \(\frac{t}{\sqrt[3]{1 + t^2}}\) with respect to \(t\), evaluated from the lower limit \(-\sqrt{x}\) to the upper limit \(x\).
In this context:
- \(g(x)\) is the integral function of \(x\).
- The numerator \(t\) signifies the variable of integration.
- The denominator is the cube root of \(1 + t^2\), which affects the rate of change of the integrand within the integral's bounds.
Transcribed Image Text:4. Differentiate a) \( g(x) = \int_{0}^{x} \cos(t^2) \, dt \)
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