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Mathematics
Mathematics
Problem
Two students each find an antiderivative of
f
(
x
)
=
4
cos
x
f(x)=4\cos x
f
(
x
)
=
4
cos
x
. One writes
F
(
x
)
=
4
sin
x
+
2
F(x)=4\sin x+2
F
(
x
)
=
4
sin
x
+
2
, while the other writes
G
(
x
)
=
−
4
sin
(
−
x
)
+
5
G(x)=-4\sin(-x)+5
G
(
x
)
=
−
4
sin
(
−
x
)
+
5
. Which of the following equals
G
(
x
)
−
F
(
x
)
G(x)-F(x)
G
(
x
)
−
F
(
x
)
for all real
x
x
x
? a)
−
8
sin
x
+
3
-8\sin x+3
−
8
sin
x
+
3
b)
−
3
-3
−
3
c)
3
3
3
d)
4
cos
x
4\cos x
4
cos
x
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