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.
Find the area of the region in the first quadrant bounded by the curves y
U
y = x, and y = 4x using the change of variables x =
integration before and after the transformation.
V
1
7
X
Y
X
y = uv. Sketch the region of
2
Reverse the order of integration and evaluate
= Homework: 6.3 Applications of Integration
Find the area of the region bounded by the curve y=x²-1 and the line y = 24!
The area is
-
Chapter 16 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
Thomas' Calculus: Early Transcendentals (14th Edition)
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