Tutorial Exercise Sketch the region of integration. Then evaluate the iterated integral. (Note that it is necessary to switch the order of integration.) XV xp . y3 dy Step 1 The given iterated integral is IT×V1+ y3 dy dx. Note that the inner limits of integration are sy< 3. Defining the region of integration as region R, then the lower and upper bounds of R are the lines y = and y = 3. Similarly, note that the outer limits of integration are 0 < x< 3, and therefore the left and right bounds of R are the lines x = 0 (or the y-axis) and x =
Tutorial Exercise Sketch the region of integration. Then evaluate the iterated integral. (Note that it is necessary to switch the order of integration.) XV xp . y3 dy Step 1 The given iterated integral is IT×V1+ y3 dy dx. Note that the inner limits of integration are sy< 3. Defining the region of integration as region R, then the lower and upper bounds of R are the lines y = and y = 3. Similarly, note that the outer limits of integration are 0 < x< 3, and therefore the left and right bounds of R are the lines x = 0 (or the y-axis) and x =
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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![### Tutorial Exercise
Sketch the region of integration. Then evaluate the iterated integral. (Note that it is necessary to switch the order of integration.)
\[
\int_{0}^{3} \int_{x}^{3} x\sqrt{1+y^3} \, dy \, dx
\]
### Step 1
The given iterated integral is
\[
\int_{0}^{3} \int_{x}^{3} x\sqrt{1+y^3} \, dy \, dx.
\]
Note that the inner limits of integration are \( x \leq y \leq 3 \).
Defining the region of integration as region \( R \), then the lower and upper bounds of \( R \) are the lines \( y = x \) and \( y = 3 \).
Similarly, note that the outer limits of integration are \( 0 \leq x \leq 3 \), and therefore the left and right bounds of \( R \) are the lines \( x = 0 \) (or the y-axis) and \( x = 3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fa7ac50-e43d-4267-956c-145cd19bd43c%2F1078c883-f7fd-4111-a185-02235c48576c%2Fd9jahjb_processed.png&w=3840&q=75)
Transcribed Image Text:### Tutorial Exercise
Sketch the region of integration. Then evaluate the iterated integral. (Note that it is necessary to switch the order of integration.)
\[
\int_{0}^{3} \int_{x}^{3} x\sqrt{1+y^3} \, dy \, dx
\]
### Step 1
The given iterated integral is
\[
\int_{0}^{3} \int_{x}^{3} x\sqrt{1+y^3} \, dy \, dx.
\]
Note that the inner limits of integration are \( x \leq y \leq 3 \).
Defining the region of integration as region \( R \), then the lower and upper bounds of \( R \) are the lines \( y = x \) and \( y = 3 \).
Similarly, note that the outer limits of integration are \( 0 \leq x \leq 3 \), and therefore the left and right bounds of \( R \) are the lines \( x = 0 \) (or the y-axis) and \( x = 3 \).
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