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.
The graphs of the function F (left, in blue) and G (right, in red) are below. Answer the following questions.
F'(1)
G'(1)
F'(6)
G'(6)
1. One of the partial fractions for
2
4x²+x-9
x3+2x²-3x
2
x+1
a) x23 b) x 1½ c) x² d)
x-1
x
is
1. One of the partial fractions for
2
2
4x²+x-9
x3+2x²-3x
a) x3 b) x11 c) x² d) z
x-1
2. Identify the improper integral.
1 x
2 x
dx
a) 3x dx b) f² 3x dx
0 3-2x
0 3-2x
x
is
c) √2^:
4
√232x dx d) fo² 3x dx
1 1
0 3-2x
B. So eax dx converges to
if
:
a) O if a0 c) - 1½ ifa 0
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.