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Mathematics
Mathematics
Problem
Suppose a curve is described by
x
=
f
(
y
)
x = f(y)
x
=
f
(
y
)
, where
f
(
y
)
≥
0
f(y) \ge 0
f
(
y
)
≥
0
for
a
≤
y
≤
b
a \le y \le b
a
≤
y
≤
b
. Which of the following expressions represents the area of the region bounded by the curve and the
y
y
y
-axis? a)
∫
a
b
f
(
y
)
d
x
\displaystyle \int_{a}^{b} f(y)\,dx
∫
a
b
f
(
y
)
d
x
b)
∫
a
b
f
(
y
)
d
y
\displaystyle \int_{a}^{b} f(y)\,dy
∫
a
b
f
(
y
)
d
y
c)
∫
f
(
a
)
f
(
b
)
y
d
x
\displaystyle \int_{f(a)}^{f(b)} y\,dx
∫
f
(
a
)
f
(
b
)
y
d
x
d)
1
2
∫
a
b
f
(
y
)
d
y
\displaystyle \tfrac12\int_{a}^{b} f(y)\,dy
2
1
∫
a
b
f
(
y
)
d
y
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