Homework Help is Here – Start Your Trial Now!
Math
Calculus
10. Find the average value of the function f(x, y) over the region R by finding f a. f(x,y)=sin(x + y) over the triangle with vertices (0,0), (0,1), (1,1). b. f(x,y) = sin² (x) over the region bounded by y = x², y = 4. c. f(x, y) = cosh (x² + y²), over the cardioid r = 2 + cose. = SSR f(x, y)dA. 11. Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. Some of the integrals may be easier in polar coordinates. a._x² + y² = a²,x≥0,y≥0,p=k(x²+y²) c. xy=4,x=1,x=4, y = 0, p = kx² L d. r=1+cos, p=k b. y cos,y=0,x=0,x==,p=k TTX L 12. Find the mass of the volume with the given density and bounded by the given surfaces. a. z = 4 x, x = 0, x = 4, y = 0, y = 4, z = 0, p(x, y, z) = ky b. z = 1 y²+12= 0, x = -2, x = 2, y = 0, y = 1, p(x, y, z) = kz 00 13. The value of the integral I = √ ex²/2dx is required in the development of the normal -00 probability density. A) use polar coordinates to evaluate the improper integral 00 1² = { [ e˜^^¿^)[ ] e˜³°³ày) = ƒ ƒe˜¨¯\^d4. B) Use that information to determine 1. -00-00

10. Find the average value of the function f(x, y) over the region R by finding f a. f(x,y)=sin(x + y) over the triangle with vertices (0,0), (0,1), (1,1). b. f(x,y) = sin² (x) over the region bounded by y = x², y = 4. c. f(x, y) = cosh (x² + y²), over the cardioid r = 2 + cose. = SSR f(x, y)dA. 11. Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. Some of the integrals may be easier in polar coordinates. a._x² + y² = a²,x≥0,y≥0,p=k(x²+y²) c. xy=4,x=1,x=4, y = 0, p = kx² L d. r=1+cos, p=k b. y cos,y=0,x=0,x==,p=k TTX L 12. Find the mass of the volume with the given density and bounded by the given surfaces. a. z = 4 x, x = 0, x = 4, y = 0, y = 4, z = 0, p(x, y, z) = ky b. z = 1 y²+12= 0, x = -2, x = 2, y = 0, y = 1, p(x, y, z) = kz 00 13. The value of the integral I = √ ex²/2dx is required in the development of the normal -00 probability density. A) use polar coordinates to evaluate the improper integral 00 1² = { [ e˜^^¿^)[ ] e˜³°³ày) = ƒ ƒe˜¨¯\^d4. B) Use that information to determine 1. -00-00

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

I need help with this problem and an explanation for the solution described below. (Calculus 3)

10. Find the average value of the function f(x, y) over the region R by finding f a. f(x,y)=sin(x + y) over the triangle with vertices (0,0), (0,1), (1,1). b. f(x,y) = sin² (x) over the region bounded by y = x², y = 4. c. f(x, y) = cosh (x² + y²), over the cardioid r = 2 + cose. = SSR f(x, y)dA. 11. Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. Some of the integrals may be easier in polar coordinates. a._x² + y² = a²,x≥0,y≥0,p=k(x²+y²) c. xy=4,x=1,x=4, y = 0, p = kx² L d. r=1+cos, p=k b. y cos,y=0,x=0,x==,p=k TTX L 12. Find the mass of the volume with the given density and bounded by the given surfaces. a. z = 4 x, x = 0, x = 4, y = 0, y = 4, z = 0, p(x, y, z) = ky b. z = 1 y²+12= 0, x = -2, x = 2, y = 0, y = 1, p(x, y, z) = kz 00 13. The value of the integral I = √ ex²/2dx is required in the development of the normal -00 probability density. A) use polar coordinates to evaluate the improper integral 00 1² = { [ e˜^^¿^)[ ] e˜³°³ày) = ƒ ƒe˜¨¯\^d4. B) Use that information to determine 1. -00-00
Transcribed Image Text:10. Find the average value of the function f(x, y) over the region R by finding f a. f(x,y)=sin(x + y) over the triangle with vertices (0,0), (0,1), (1,1). b. f(x,y) = sin² (x) over the region bounded by y = x², y = 4. c. f(x, y) = cosh (x² + y²), over the cardioid r = 2 + cose. = SSR f(x, y)dA. 11. Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. Some of the integrals may be easier in polar coordinates. a._x² + y² = a²,x≥0,y≥0,p=k(x²+y²) c. xy=4,x=1,x=4, y = 0, p = kx² L d. r=1+cos, p=k b. y cos,y=0,x=0,x==,p=k TTX L 12. Find the mass of the volume with the given density and bounded by the given surfaces. a. z = 4 x, x = 0, x = 4, y = 0, y = 4, z = 0, p(x, y, z) = ky b. z = 1 y²+12= 0, x = -2, x = 2, y = 0, y = 1, p(x, y, z) = kz 00 13. The value of the integral I = √ ex²/2dx is required in the development of the normal -00 probability density. A) use polar coordinates to evaluate the improper integral 00 1² = { [ e˜^^¿^)[ ] e˜³°³ày) = ƒ ƒe˜¨¯\^d4. B) Use that information to determine 1. -00-00
Expert Solution
steps

Step by step

Solved in 2 steps with 10 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