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Mathematics
Mathematics
Problem
Let
F
(
x
)
F(x)
F
(
x
)
be an antiderivative of
f
(
x
)
=
−
3
(
2
x
3
−
5
sin
x
+
4
e
x
)
f(x)=-3\bigl(2x^{3}-5\sin x+4e^{x}\bigr)
f
(
x
)
=
−
3
(
2
x
3
−
5
sin
x
+
4
e
x
)
. Given that
F
(
0
)
=
4
F(0)=4
F
(
0
)
=
4
, answer the following: a. (i) Find the general form of
F
(
x
)
F(x)
F
(
x
)
. b. (ii) Determine the particular
F
(
x
)
F(x)
F
(
x
)
satisfying
F
(
0
)
=
4
F(0)=4
F
(
0
)
=
4
.
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