In Problems 33–38, evaluate each integral. Graph the region of integration , reverse the order of integration, and then evaluate the integral with the order reversed. 35. ∫ 0 1 ∫ 0 1 − x 2 x y d y d x
In Problems 33–38, evaluate each integral. Graph the region of integration , reverse the order of integration, and then evaluate the integral with the order reversed. 35. ∫ 0 1 ∫ 0 1 − x 2 x y d y d x
Solution Summary: The author evaluates the iterated integral by graphing the region of integration and reverse the order of the integration.
In Problems 33–38, evaluate each integral. Graph the region of integration, reverse the order of integration, and then evaluate the integral with the order reversed.
35.
∫
0
1
∫
0
1
−
x
2
x
y
d
y
d
x
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.
An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of the
region is growing at a rate of 24 m per year at a time when the region is 460 m wide.
[Select]
V
Which of the following variables will correctly represent the
problem?
A. length = x, width = 2x, d =
= 24
B. length = 2x, width = x,
= 24
C. length = x, width = 2x,
=
= 24
dy
D. length = 2x, width = x,
= 24
[Select]
What is the appropriate equation for the missing rate?
= 2x² da
= 4x
= 2x²
= 4x
How fast is the area changing at the given point in time?
A.
B.
C. d
D.
[Select]
A. d=10156800 square meters per year
dy
B.
10156800 square meters per year
dt
C. d
= 44160 square meters per year
D
44160 square meters per year
dy
dt
In Problems 17–36, use Theorem 2 to find the local extrema.
Obtain
characteristics
for
y2 Uxx + Uyy =
%3D
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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