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Mathematics
Mathematics
Problem
Describe, in one or two sentences, why the definite integral
∫
a
b
h
(
x
)
w
(
x
)
d
x
\displaystyle \int_{a}^{b} h(x)\,w(x)\,dx
∫
a
b
h
(
x
)
w
(
x
)
d
x
represents the exact volume of a solid whose cross sections perpendicular to the
x
x
x
-axis are rectangles with height
h
(
x
)
h(x)
h
(
x
)
and base width
w
(
x
)
w(x)
w
(
x
)
on the interval
[
a
,
b
]
[a,b]
[
a
,
b
]
.
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