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. 33. ∬ R ( y − x y + 2 x + 1 ) 4 d A , where R is the parallelogram bounded by y – x = 1, y – x = 2, y + 2 x = 0, and y + 2 x = 4
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. 33. ∬ R ( y − x y + 2 x + 1 ) 4 d A , where R is the parallelogram bounded by y – x = 1, y – x = 2, y + 2 x = 0, and y + 2 x = 4
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.
33.
∬
R
(
y
−
x
y
+
2
x
+
1
)
4
d
A
, where R is the parallelogram bounded by y – x = 1, y – x = 2, y + 2x = 0, and y + 2x = 4
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.
The graph of g consists of two straight lines and a semicircle as shown in the figure.
y
20
y = g(x)
10
20
Evaluate each integral by interpreting it in terms of areas.
9(x) dx
(b)
9(x) dx
(c) 9(x) dx
TRANSFER
TRAN SFER
ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION
Direction: Evaluate the following integrals.
1. S dx
Vx
2. S dx
Sketch the region of integration and change the order of integration.
3 √9 - y²
Br
-3 JO
f(x, y) dx dy
f(x, y) dy dx
Thomas' Calculus: Early Transcendentals (14th Edition)
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