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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
3
x
2
−
6
x
+
4
f(x)=3x^{2}-6x+4
f
(
x
)
=
3
x
2
−
6
x
+
4
for
1
≤
x
≤
4
1\le x\le 4
1
≤
x
≤
4
. (a) Find an antiderivative
F
(
x
)
F(x)
F
(
x
)
of
f
(
x
)
f(x)
f
(
x
)
that satisfies
F
(
0
)
=
0
F(0)=0
F
(
0
)
=
0
. (b) Calculate the exact value of
∫
1
4
f
(
x
)
d
x
\displaystyle \int_{1}^{4} f(x)\,dx
∫
1
4
f
(
x
)
d
x
. (c) Interpret the result from part (b) as a geometric quantity. Include appropriate units in your statement.
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