Homework Help is Here – Start Your Trial Now!
Math
Calculus
a) 2₂x5e-x² dx b) 510 cos(5t) dt

a) 2₂x5e-x² dx b) 510 cos(5t) dt

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
Please solve 1. (a) and (b), thanks!
**Exam 2: Topics and Exercises** **Topics Covered:** 1. Areas and definite integrals 2. Volumes by slicing 3. Arc lengths and surface areas 4. Integration by substitution 5. Integration by parts 6. Integrals of trigonometric functions and trigonometric substitution 7. Partial fractions 8. Improper integrals **Exercises:** 1. **Evaluate each definite integral** (Hint: very few calculations are required for these problems, a graph will be helpful) a) \(\int_{2}^{\infty} x^2 e^{-x^2} \, dx\) b) \(\int_{0}^{2\pi/5} 10 \cos(5t) \, dt\) c) \(\int_{-3}^{3} \sqrt{9-x^2} \, dx\) d) \(\int_{1}^{2} 2 + \sqrt{1 - x^2} \, dx\) e) \(\int_{-4}^{4} \sqrt{9 - (x + 1)^2} \, dx\) Possible answers: - a) 0 - b) 0 - c) \(-\frac{9\pi}{2}\) - d) \(4 + \frac{\pi}{2}\) - e) \(\frac{9\pi}{2}\) 2. **Consider the curve \(y = \frac{1}{3}(x^2 + 2)^{3/2}\), \(0 \leq x \leq 1\)** a) Find the length of this curve b) Find the volume of the solid of revolution obtained by rotating the curve around the x-axis Answers: - a) \(L = \frac{4}{3}\) - b) \(V = \frac{467}{315} \, \text{cu. units}\) 3. **Find the volume of the solid obtained by rotating the region bounded by \(y = \frac{1}{4} x^2\), \(x = 2\), and \(y = 0\) about the y-axis**
Transcribed Image Text:**Exam 2: Topics and Exercises** **Topics Covered:** 1. Areas and definite integrals 2. Volumes by slicing 3. Arc lengths and surface areas 4. Integration by substitution 5. Integration by parts 6. Integrals of trigonometric functions and trigonometric substitution 7. Partial fractions 8. Improper integrals **Exercises:** 1. **Evaluate each definite integral** (Hint: very few calculations are required for these problems, a graph will be helpful) a) \(\int_{2}^{\infty} x^2 e^{-x^2} \, dx\) b) \(\int_{0}^{2\pi/5} 10 \cos(5t) \, dt\) c) \(\int_{-3}^{3} \sqrt{9-x^2} \, dx\) d) \(\int_{1}^{2} 2 + \sqrt{1 - x^2} \, dx\) e) \(\int_{-4}^{4} \sqrt{9 - (x + 1)^2} \, dx\) Possible answers: - a) 0 - b) 0 - c) \(-\frac{9\pi}{2}\) - d) \(4 + \frac{\pi}{2}\) - e) \(\frac{9\pi}{2}\) 2. **Consider the curve \(y = \frac{1}{3}(x^2 + 2)^{3/2}\), \(0 \leq x \leq 1\)** a) Find the length of this curve b) Find the volume of the solid of revolution obtained by rotating the curve around the x-axis Answers: - a) \(L = \frac{4}{3}\) - b) \(V = \frac{467}{315} \, \text{cu. units}\) 3. **Find the volume of the solid obtained by rotating the region bounded by \(y = \frac{1}{4} x^2\), \(x = 2\), and \(y = 0\) about the y-axis**
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS