Integration as an Accumulation Process In Exercises 53-56, find the accumulation function F. Then evaluate F at each value of the independent variable and graphically. show the area given by each value of the independent variable. F ( x ) = ∫ 0 t ( 1 2 t 2 + 2 ) d t ( a ) F ( 0 ) ( b ) F ( 4 ) ( c ) F ( 6 )
Integration as an Accumulation Process In Exercises 53-56, find the accumulation function F. Then evaluate F at each value of the independent variable and graphically. show the area given by each value of the independent variable. F ( x ) = ∫ 0 t ( 1 2 t 2 + 2 ) d t ( a ) F ( 0 ) ( b ) F ( 4 ) ( c ) F ( 6 )
Solution Summary: The author explains how to calculate the accumulation function F and evaluate F at each value of the independent variable.
Integration as an Accumulation Process In Exercises 53-56, find the accumulation function F. Then evaluate F at each value of the independent variable and graphically. show the area given by each value of the independent variable.
F
(
x
)
=
∫
0
t
(
1
2
t
2
+
2
)
d
t
(
a
)
F
(
0
)
(
b
)
F
(
4
)
(
c
)
F
(
6
)
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.
Let f be a function whose graph consists of 5 line segments and a semicircle as shown in the figure below.
Let g(x) = √ƒƒ(t) dt .
0
3
2
-2
2
4
5
6
7
8
9
10
11
12
13
14
15
1. g(0) =
2. g(2) =
3. g(4) =
4. g(6) =
5. g'(3) =
6. g'(13)=
The expression 3 | (3+1/+1)
of the following integrals?
A
Ов
E
+
+
+ +
18
3+1+1
3++1
3++1
(A) √2×14 dx
x+1
(C) 1½-½√ √ ² ( 14 ) d x
(B) √31dx
(D) So 3+x
-dx
is a Riemann sum approximation of which
5
(E) 1½√√3dx
2x+1
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
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