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. 34. ∬ R e x y d A , where R is the region bounded by the hyperbolas xy = 1 and xy = 4, and the lines y / x = 1 and y / x = 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. 34. ∬ R e x y d A , where R is the region bounded by the hyperbolas xy = 1 and xy = 4, and the lines y / x = 1 and y / x = 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.
34.
∬
R
e
x
y
d
A
, where R is the region bounded by the hyperbolas xy = 1 and xy = 4, and the lines y/x = 1 and y/x = 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.
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
Consider the following.
y
1
2
4
х— 3
-1
x - 3 x
(a) Find the points of intersection of the curves.
(x, y) =
(smaller x-value)
(х, у) %3D
(larger x-value)
(b) Form the integral that represents the area of the shaded region.
dx
(c) Find the area of the shaded region. (Give an exact answer. Do not round.)
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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