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.
TRANSFER
TRAN SFER
ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION
Direction: Evaluate the following integrals.
1. S dx
Vx
2. S dx
x dx
V 1-x2
find the value ?
Specify the integral varieties?
Using the method of u-substitution,
Se
(6x - 8) dx = = [₁ f
where
U=
du =
a=
b=
f(u) =
f(u) du
(enter a function of x)
da (enter a function of x)
(enter a number)
(enter a number)
(enter a function of u).
The value of the original integral is
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University Calculus: Early Transcendentals (3rd Edition)
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