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...
Related questions
Question
![**Problem Statement:**
Find the area between the graph of \( x = \frac{1}{y^2} \) and the y-axis on the interval \([1, 4]\).
**Graph Description:**
The graph provided shows a curve representing the function \( x = \frac{1}{y^2} \). It is a downward-sloping curve starting from \( y = 1 \) to \( y = 4 \). The area between this curve and the y-axis is shaded, indicating the region for which the area needs to be calculated. The x-axis range is from \(-0.5\) to \(1.5\), while the y-axis range is from \(0\) to \(4\).
**Solution Approach:**
To find the area, set up the integral of the function \( x = \frac{1}{y^2} \) with respect to \( y \) from \( y = 1 \) to \( y = 4 \).
\[
\text{Area} = \int_{1}^{4} \frac{1}{y^2} \, dy
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa18a6723-a2ab-43ae-9c9a-35233fc8cb89%2F8465861e-5375-4ceb-ac81-a98ff6bafdf2%2F0elxmb0l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the area between the graph of \( x = \frac{1}{y^2} \) and the y-axis on the interval \([1, 4]\).
**Graph Description:**
The graph provided shows a curve representing the function \( x = \frac{1}{y^2} \). It is a downward-sloping curve starting from \( y = 1 \) to \( y = 4 \). The area between this curve and the y-axis is shaded, indicating the region for which the area needs to be calculated. The x-axis range is from \(-0.5\) to \(1.5\), while the y-axis range is from \(0\) to \(4\).
**Solution Approach:**
To find the area, set up the integral of the function \( x = \frac{1}{y^2} \) with respect to \( y \) from \( y = 1 \) to \( y = 4 \).
\[
\text{Area} = \int_{1}^{4} \frac{1}{y^2} \, dy
\]
Expert Solution
Step 1: given
to find the area between the curve x=1/y^2 and y axis in tge interval [1,4]
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning