Double integrals—your choice of transformation Evaluate the following integrals using a change of variables. Sketch the original and new regions of integration , R and S. 36. ∬ R ( x − y ) x − 2 y d A , where R is the triangular region bounded by y = 0, x – 2 y = 0, and x – y = 1
Double integrals—your choice of transformation Evaluate the following integrals using a change of variables. Sketch the original and new regions of integration , R and S. 36. ∬ R ( x − y ) x − 2 y d A , where R is the triangular region bounded by y = 0, x – 2 y = 0, and x – y = 1
Solution Summary: The author evaluates the integral and sketches the original and new region. The Jacobian transformation T is cJ(u,v)
Double integrals—your choice of transformationEvaluate the following integrals using a change of variables. Sketch the original and new regions of integration, R and S.
36.
∬
R
(
x
−
y
)
x
−
2
y
d
A
, where R is the triangular region bounded by y = 0, x – 2y = 0, and x – y = 1
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.
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
Chapter 13 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
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