For these problems, the most important sketch is the projection in the plane of integration , which is easy to do by hand. However, you might like to use your computer to plot the corresponding 3 dimensional picture. Find the area of the plane x − 2 y + 5 z = 13 cut out by the cylinder x 2 + y 2 = 9 .
For these problems, the most important sketch is the projection in the plane of integration , which is easy to do by hand. However, you might like to use your computer to plot the corresponding 3 dimensional picture. Find the area of the plane x − 2 y + 5 z = 13 cut out by the cylinder x 2 + y 2 = 9 .
For these problems, the most important sketch is the projection in the plane of integration, which is easy to do by hand. However, you might like to use your computer to plot the corresponding 3 dimensional picture.
Find the area of the plane
x
−
2
y
+
5
z
=
13
cut out by the cylinder
x
2
+
y
2
=
9
.
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
Use the change in variables
s = x + 4y, t = y to find the area of the ellipse
x^2 + 8xy + 17y^2, less than or equal to 1.
Calculate (4x² + 5e³) dy, where C is the triangle of vertices (0,0), (2,0) and (2,2).
[(4x²+
Note: For a triangle, parameterize each side as a line segment, and calculate the line integral on
that side. Then, add up all of the answers for each side to find the final answer. Make sure to go in
order, from the first point to the second point, then from the second point to the third point, and then
from the third point back to the first point, because the order does matter.
5e) dy =
The equation of the line touching both the parabolas y² = 4x
%3D
and x' = -32y is x-2y+2 = 0, then a is
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