Integration as an Accumulation Process In Exercises 53-56, find the accumulation function F. Then evaluate F of 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 + 1 ) d t ( a ) F ( 0 ) ( b ) F ( 2 ) ( c ) F ( 6 )
Integration as an Accumulation Process In Exercises 53-56, find the accumulation function F. Then evaluate F of 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 + 1 ) d t ( a ) F ( 0 ) ( b ) F ( 2 ) ( 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 of 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
+
1
)
d
t
(
a
)
F
(
0
)
(
b
)
F
(
2
)
(
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.
8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.
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13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.
DO NOT GIVE THE WRONG ANSWER
SHOW ME ALL THE NEEDED STEPS
11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
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