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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![### Change the Order of Integration
Consider the integral:
\[ \int_{-1}^{\pi/2} \int_{0}^{x + 1} 3 \sin(x) \, dy \, dx \]
Here are the options for changing the order of integration:
1. \[ \int_{-1}^{\pi/2 + 1} \int_{y - 1}^{x + 1} 3 \sin(x) \, dx \, dy \]
2. \[ \int_{-1}^{0} \int_{0}^{\pi/2 + 1} 3 \sin(x) \, dx \, dy \]
3. \[ \int_{( \pi/2 )}^{\pi/2 + 1} \int_{y - 1}^{3 \sin(x)} \, dx \, dy \]
4. \[ \int_{( \pi/2 )}^{0} \int_{x + 1}^{\pi/2 + 1} 3 \sin(x) \, dy \, dx \]
5. \[ \int_{0}^{\pi/2} \int_{y - 1}^{\pi/2} 3 \sin(x) \, dx \, dy \]
### Evaluate the Integral
\[ \boxed{} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad35cd49-88f1-4759-9e4c-232c0c792d3e%2Fe472ce51-e544-4efd-b0ce-76eaaad448a2%2F4y111wl.jpeg&w=3840&q=75)
Transcribed Image Text:### Change the Order of Integration
Consider the integral:
\[ \int_{-1}^{\pi/2} \int_{0}^{x + 1} 3 \sin(x) \, dy \, dx \]
Here are the options for changing the order of integration:
1. \[ \int_{-1}^{\pi/2 + 1} \int_{y - 1}^{x + 1} 3 \sin(x) \, dx \, dy \]
2. \[ \int_{-1}^{0} \int_{0}^{\pi/2 + 1} 3 \sin(x) \, dx \, dy \]
3. \[ \int_{( \pi/2 )}^{\pi/2 + 1} \int_{y - 1}^{3 \sin(x)} \, dx \, dy \]
4. \[ \int_{( \pi/2 )}^{0} \int_{x + 1}^{\pi/2 + 1} 3 \sin(x) \, dy \, dx \]
5. \[ \int_{0}^{\pi/2} \int_{y - 1}^{\pi/2} 3 \sin(x) \, dx \, dy \]
### Evaluate the Integral
\[ \boxed{} \]
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