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
![### Integration Problem
**Problem Statement:**
Integrate the following function:
\[ \int 200e^{0.02x} \, dx \]
**Solution:**
To solve for the integral of the function, let's follow these steps:
The given integral is:
\[ \int 200e^{0.02x} \, dx \]
Recall the integral of \(e^{kx}\), which is \(\frac{1}{k}e^{kx}\). Here \( k = 0.02 \).
Applying this knowledge:
\[ \int e^{0.02x} \, dx = \frac{1}{0.02}e^{0.02x} + C \]
So, including the constant 200:
\[ \int 200e^{0.02x} \, dx = 200 \cdot \frac{1}{0.02}e^{0.02x} + C \]
Simplifying the constants:
\[ 200 \cdot \frac{1}{0.02} = 200 \cdot 50 = 10000 \]
Thus, the integral becomes:
\[ \int 200e^{0.02x} \, dx = 10000e^{0.02x} + C \]
Finally, the integral is:
\[ \int 200e^{0.02x} \, dx = 10000e^{0.02x} + C \]
You can enter this final expression in the provided box along with the constant of integration, \( + C \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa532d6c3-fc4a-4c4d-b082-7cb1920e9739%2F3b92c462-eb5a-47f5-9dd6-4408a29dc527%2Fo5sh542f_processed.png&w=3840&q=75)
Transcribed Image Text:### Integration Problem
**Problem Statement:**
Integrate the following function:
\[ \int 200e^{0.02x} \, dx \]
**Solution:**
To solve for the integral of the function, let's follow these steps:
The given integral is:
\[ \int 200e^{0.02x} \, dx \]
Recall the integral of \(e^{kx}\), which is \(\frac{1}{k}e^{kx}\). Here \( k = 0.02 \).
Applying this knowledge:
\[ \int e^{0.02x} \, dx = \frac{1}{0.02}e^{0.02x} + C \]
So, including the constant 200:
\[ \int 200e^{0.02x} \, dx = 200 \cdot \frac{1}{0.02}e^{0.02x} + C \]
Simplifying the constants:
\[ 200 \cdot \frac{1}{0.02} = 200 \cdot 50 = 10000 \]
Thus, the integral becomes:
\[ \int 200e^{0.02x} \, dx = 10000e^{0.02x} + C \]
Finally, the integral is:
\[ \int 200e^{0.02x} \, dx = 10000e^{0.02x} + C \]
You can enter this final expression in the provided box along with the constant of integration, \( + C \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 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