In the following exercises, use the transformation y − x = u , x + y = v to evaluate the integrals on the lines y = x , y = − x + 2 , y = x + 2 . and y = − x shown in the following figure. 392. ∬ R e x + y d A
In the following exercises, use the transformation y − x = u , x + y = v to evaluate the integrals on the lines y = x , y = − x + 2 , y = x + 2 . and y = − x shown in the following figure. 392. ∬ R e x + y d A
In the following exercises, use the transformation
y
−
x
=
u
,
x
+
y
=
v
to evaluate the integrals on the lines
y
=
x
,
y
=
−
x
+
2
,
y
=
x
+
2
. and
y
=
−
x
shown in the following figure.
392.
∬
R
e
x
+
y
d
A
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.
Use the given transformation to evaluate the integral.
J (15x + 10y) dA, where R is the parallelogram with vertices (-2, 8), (2, -8), (3, -7), and (-1, 9) ; x =
(u + v), y = (v - 4u)
Use the given transformation to evaluate the integral.
JS (20x + 15y) dA, where R is the parallelogram with vertices (−3, 12), (3, −12), (6, −9), and (0, 15); x =
= = = (u + v), y = =—=— (v - 4u)
Let F = (1yz)i + (5xz)j + (1xy) k. Compute the following:
A. div F =
B. curl F =
C. div curl F
i+
j+
Note: Your answers should be expressions of x, y and/or z; e.g. "3xy" or "z" or "5"
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01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY