Double integrals—transformation given To evaluate the following integrals, carry out the following steps . a. Sketch the original region of integration R and the new region S using the given change of variables . b. Find the limits of integration for the new integral with respect to u and v . c. Compute the Jacobian . d. Chance variables and evaluate the new integral . 76. ∬ R x y 2 d A ; R is the region between the hyperbolas xy = 1 and xy = 4 and the lines y = 1 and y = 4; use x = u / v , y = v .
Double integrals—transformation given To evaluate the following integrals, carry out the following steps . a. Sketch the original region of integration R and the new region S using the given change of variables . b. Find the limits of integration for the new integral with respect to u and v . c. Compute the Jacobian . d. Chance variables and evaluate the new integral . 76. ∬ R x y 2 d A ; R is the region between the hyperbolas xy = 1 and xy = 4 and the lines y = 1 and y = 4; use x = u / v , y = v .
Solution Summary: The author illustrates the region R in xy- and uv- plane.
Double integrals—transformation givenTo evaluate the following integrals, carry out the following steps.
a. Sketch the original region of integration R and the new region S using the given change of variables.
b. Find the limits of integration for the new integral with respect to u and v.
c. Compute the Jacobian.
d.Chance variables and evaluate the new integral.
76.
∬
R
x
y
2
d
A
;
R is the region between the hyperbolas xy = 1 and xy = 4 and the lines y = 1 and y = 4; use x = u/v, y = v.
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Question 2.
i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) =
P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y
have the same distribution? Explain your answer.
ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random
variable? Do X and Y have the same distribution? Explain your answer.
Problem 4. Let
f(x, y) =
{
Find P(X <1/2|Y = 1/2).
c(x + y²) 0
Qize
f(x)
x + 2x2 - 2
x² + 4x² - 4
Solve the equation using Newton
Raphson
Chapter 13 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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