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. 73. ∬ x y 2 d A ; R = { ( x , y ) : y / 3 ≤ x ≤ ( y + 6 ) / 3 , 0 ≤ y ≤ 3 } ; use x = u + v / 3 , 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. 73. ∬ x y 2 d A ; R = { ( x , y ) : y / 3 ≤ x ≤ ( y + 6 ) / 3 , 0 ≤ y ≤ 3 } ; use x = u + v / 3 , y = v .
Solution Summary: The author illustrates the region R in xy- and uv-planes.
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.
73.
∬
x
y
2
d
A
;
R
=
{
(
x
,
y
)
:
y
/
3
≤
x
≤
(
y
+
6
)
/
3
,
0
≤
y
≤
3
}
;
use
x
=
u
+
v
/
3
,
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.
A:ME
Assignment #8..
Code: ENG122
University of Mosul
Mechanical Engincering
Mathematics II
Year:2020- 2021
Instructors: Dr, Omar Sallahaldeen
and T.A. Suha Hashim
ASSIGNMENT #8
Calculate the following integrals-:
9x-
x - x
1-
2-
16x
dx
4x - 4x + 1
3-
4-
dy
5-
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
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Numerical Integration Introduction l Trapezoidal Rule Simpson's 1/3 Rule l Simpson's 3/8 l GATE 2021; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=zadUB3NwFtQ;License: Standard YouTube License, CC-BY