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
![**Problem Statement:**
Find \(\frac{dy}{dx}\) for
\[
y = \int_{0}^{x} \sqrt{11 + 12t^2} \, dt.
\]
**Solution:**
Determine \(\frac{dy}{dx}\):
\[
\frac{dy}{dx} = \sqrt{11 + 12x^2}.
\]
Note: This solution applies the Fundamental Theorem of Calculus, which states that if \(y\) is defined as an integral from a constant to \(x\), then \(\frac{dy}{dx}\) is the integrand evaluated at \(x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93ade889-6aa6-440d-b6d3-23ce5a98ca6e%2Fca7141cf-1f03-4411-b867-85d014ef44e3%2F34a4q2e_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \(\frac{dy}{dx}\) for
\[
y = \int_{0}^{x} \sqrt{11 + 12t^2} \, dt.
\]
**Solution:**
Determine \(\frac{dy}{dx}\):
\[
\frac{dy}{dx} = \sqrt{11 + 12x^2}.
\]
Note: This solution applies the Fundamental Theorem of Calculus, which states that if \(y\) is defined as an integral from a constant to \(x\), then \(\frac{dy}{dx}\) is the integrand evaluated at \(x\).
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