Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be useful. 13. ∭ D ( x y + x z + y z ) d V ; D = { ( x , y , z ) : − 1 ≤ x ≤ 1 , − 2 ≤ y ≤ 2 , − 3 ≤ z ≤ 3 }
Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be useful. 13. ∭ D ( x y + x z + y z ) d V ; D = { ( x , y , z ) : − 1 ≤ x ≤ 1 , − 2 ≤ y ≤ 2 , − 3 ≤ z ≤ 3 }
Integrals over boxesEvaluate the following integrals. A sketch of the region of integration may be useful.
13.
∭
D
(
x
y
+
x
z
+
y
z
)
d
V
;
D
=
{
(
x
,
y
,
z
)
:
−
1
≤
x
≤
1
,
−
2
≤
y
≤
2
,
−
3
≤
z
≤
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.
After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked,
its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released.
s(t)=-16t² + 30t+3
a. How high will it go?
b. How long is it in the air?
+6x²+135x+1) (0≤x≤10). a) Find the number of units
The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x²+6x² + 135x+
that should be sold in order to maximize the total profit. b) What is the maximum profit?
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the
population in the year 2000 was 22600.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
Chapter 16 Solutions
Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
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