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Mathematics
Mathematics
Problem
Let
f
(
x
)
≤
0
f(x)\le 0
f
(
x
)
≤
0
for all
x
x
x
in
[
p
,
q
]
[p,q]
[
p
,
q
]
. Which of the following equals the area of the region enclosed by
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
, the
x
x
x
-axis, and the lines
x
=
p
x=p
x
=
p
and
x
=
q
x=q
x
=
q
? a)
∫
q
p
f
(
x
)
d
x
\displaystyle \int_q^p f(x)\,dx
∫
q
p
f
(
x
)
d
x
b)
1
2
∫
p
q
f
(
x
)
d
x
\displaystyle \dfrac12\int_p^q f(x)\,dx
2
1
∫
p
q
f
(
x
)
d
x
c)
∫
p
q
(
−
f
(
x
)
)
d
x
\displaystyle \int_p^q \bigl(-f(x)\bigr)\,dx
∫
p
q
(
−
f
(
x
)
)
d
x
d)
∫
p
q
f
(
x
)
d
x
\displaystyle \int_p^q f(x)\,dx
∫
p
q
f
(
x
)
d
x
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