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.
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11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
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The sides of a cube of ice are melting at a rate of 1 inch per hour. When its volume is 64 cubic inches, at what rate is its volume changing?
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