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. 35. ∬ R x y d A , where R is the region bounded by the hyperbolas xy = 1 and xy = 4, and the lines y = 1 and y = 3
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. 35. ∬ R x y d A , where R is the region bounded by the hyperbolas xy = 1 and xy = 4, and the lines y = 1 and y = 3
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.
35.
∬
R
x
y
d
A
, where R is the region bounded by the hyperbolas xy = 1 and xy = 4, and the lines y = 1 and y = 3
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
Locate the centroid of the shaded area between the two curves.
Consider the following.
y
y = x° - 2 x
4
2
X
-4
-2
4
-2
y = 2 x
-4
-6
(a) Find the points of intersection of the curves.
(х, у) %3D (
(smallest x-value)
(х, у)
(х, у)
(largest y-value)
(b) Form the integral that represents the area of the shaded region.
0.
2
dx +
dx
2
(c) Find the area of the shaded region.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY