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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![### Evaluating Definite Integrals
#### Problem Statement
Evaluate each definite integral using any method. Verify on the calculator.
#### Definite Integrals to Evaluate:
(b) \[ \int_{1}^{4} 3\sqrt{x} \, dx \]
(c) \[ \int_{0}^{\pi/4} \sec^2{x} \, dx \]
(d) \[ \int_{0}^{2} |2x - 1| \, dx \]
#### Explanation:
**Integral (b):**
You need to find the definite integral of \(3\sqrt{x}\) from 1 to 4.
**Integral (c):**
You need to find the definite integral of \(\sec^2{x}\) from 0 to \(\pi/4\).
**Integral (d):**
You need to find the definite integral of \(|2x - 1|\) from 0 to 2, which involves evaluating the absolute value function in the given interval.
#### Verification:
After solving each integral using any preferred method (e.g., substitution, integration by parts, fundamental theorem of calculus, etc.), verify your results using a graphing calculator or an integral calculator for accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefc33f9d-fbf7-459e-8db8-0e4a73348f29%2Fd1f0979e-29d6-480e-b3a3-22970dfc20f5%2F41jv44q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Definite Integrals
#### Problem Statement
Evaluate each definite integral using any method. Verify on the calculator.
#### Definite Integrals to Evaluate:
(b) \[ \int_{1}^{4} 3\sqrt{x} \, dx \]
(c) \[ \int_{0}^{\pi/4} \sec^2{x} \, dx \]
(d) \[ \int_{0}^{2} |2x - 1| \, dx \]
#### Explanation:
**Integral (b):**
You need to find the definite integral of \(3\sqrt{x}\) from 1 to 4.
**Integral (c):**
You need to find the definite integral of \(\sec^2{x}\) from 0 to \(\pi/4\).
**Integral (d):**
You need to find the definite integral of \(|2x - 1|\) from 0 to 2, which involves evaluating the absolute value function in the given interval.
#### Verification:
After solving each integral using any preferred method (e.g., substitution, integration by parts, fundamental theorem of calculus, etc.), verify your results using a graphing calculator or an integral calculator for accuracy.
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