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Mathematics
Problem
Evaluate the integral
∫
0
4
f
(
x
)
d
x
where
f
(
x
)
=
{
3
x
,
0
≤
x
≤
2
,
8
−
2
x
,
2
<
x
≤
4.
\int_{0}^{4} f(x)\,dx \quad\text{where}\quad f(x)=\begin{cases}3x, & 0\le x\le 2,\\ 8-2x, & 2< x\le 4.\end{cases}
∫
0
4
f
(
x
)
d
x
where
f
(
x
)
=
{
3
x
,
8
−
2
x
,
0
≤
x
≤
2
,
2
<
x
≤
4.
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