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Mathematics
Problem
For a continuous function
f
f
f
, let
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
g(x)=\int_{0}^{x} f(t)\,dt
g
(
x
)
=
∫
0
x
f
(
t
)
d
t
. You are given
g
(
3
)
=
8
g(3)=8
g
(
3
)
=
8
,
g
(
12
)
=
−
2
g(12)=-2
g
(
12
)
=
−
2
, and
∫
3
7
f
(
t
)
d
t
=
−
5
\displaystyle \int_{3}^{7} f(t)\,dt=-5
∫
3
7
f
(
t
)
d
t
=
−
5
. What is the value of
∫
7
12
f
(
t
)
d
t
\displaystyle \int_{7}^{12} f(t)\,dt
∫
7
12
f
(
t
)
d
t
? a)
−
15
-15
−
15
b)
10
10
10
c)
−
5
-5
−
5
d)
5
5
5
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