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Mathematics
Problem
Explain why the definite integral
∫
a
b
f
(
x
)
d
x
\int_a^b f(x)\,dx
∫
a
b
f
(
x
)
d
x
may fail to equal the geometric area between the curve
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
and the x-axis when
f
(
x
)
f(x)
f
(
x
)
takes both positive and negative values on
[
a
,
b
]
[a,b]
[
a
,
b
]
.
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