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Mathematics
Problem
Explain in one or two sentences why, if
f
(
x
)
≥
0
f(x)\ge 0
f
(
x
)
≥
0
on
[
a
,
b
]
[a,b]
[
a
,
b
]
, the definite integral
∫
a
b
f
(
x
)
d
x
\int_a^b f(x)\,dx
∫
a
b
f
(
x
)
d
x
equals the geometric area enclosed by the curve
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
, the
x
x
x
-axis, and the lines
x
=
a
x=a
x
=
a
and
x
=
b
x=b
x
=
b
.
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