C Evaluate each double integral in Problems 39–42. Select the order of integration carefully; each problem is easy to do one way and difficult the other. 40. ∬ R x y e x 2 y d A ; R = { ( x , y ) | 0 ≤ x ≤ 1 , 1 ≤ y ≤ 2 }
C Evaluate each double integral in Problems 39–42. Select the order of integration carefully; each problem is easy to do one way and difficult the other. 40. ∬ R x y e x 2 y d A ; R = { ( x , y ) | 0 ≤ x ≤ 1 , 1 ≤ y ≤ 2 }
Solution Summary: The author evaluates the value of the iterated integral by letting u=x2y, then its derivative is du=2xydx.
CEvaluate each double integral in Problems 39–42. Select the order of integration carefully; each problem is easy to do one way and difficult the other.
40.
∬
R
x
y
e
x
2
y
d
A
;
R
=
{
(
x
,
y
)
|
0
≤
x
≤
1
,
1
≤
y
≤
2
}
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.
In Problems 85–90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zerocorrect to two decimal places.
23. What is the domain of the function f(x) = Vx² – 16?
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In Problems 25–32, use the given functions f and g.
(a) Solve f(x) = 0.
(e) Solve g(x) s 0.
(b) Solve g(x) = 0.
(f) Solve f(x) >g(x).
Chapter 7 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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