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
q4
![**Evaluate the Double Integral**
Given the problem, we need to evaluate the double integral:
\[
\int_{0}^{9} \int_{-5}^{2} (8x + y) \, dx \, dy
\]
Here's the structure of the integral:
- The outer integral is with respect to \( y \) and spans from 0 to 9.
- The inner integral is with respect to \( x \) and spans from -5 to 2.
**Solution Steps:**
1. **Inner Integral:** Compute the integral of \( 8x + y \) with respect to \( x \), treating \( y \) as a constant.
2. **Outer Integral:** After finding the result of the inner integral, integrate that result with respect to \( y \).
The problem requires the solution to be simplified fully.
**Graphical Interpretation:**
There are no graphs or diagrams provided in this problem. The task is purely computational, focused on solving the given double integral step by step.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37b0c948-1d0a-44d2-bf5d-6afda18ee4f9%2F5f6bbef1-159f-4215-955d-74326cb16b86%2Fweb24ig_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the Double Integral**
Given the problem, we need to evaluate the double integral:
\[
\int_{0}^{9} \int_{-5}^{2} (8x + y) \, dx \, dy
\]
Here's the structure of the integral:
- The outer integral is with respect to \( y \) and spans from 0 to 9.
- The inner integral is with respect to \( x \) and spans from -5 to 2.
**Solution Steps:**
1. **Inner Integral:** Compute the integral of \( 8x + y \) with respect to \( x \), treating \( y \) as a constant.
2. **Outer Integral:** After finding the result of the inner integral, integrate that result with respect to \( y \).
The problem requires the solution to be simplified fully.
**Graphical Interpretation:**
There are no graphs or diagrams provided in this problem. The task is purely computational, focused on solving the given double integral step by step.
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