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Mathematics
Mathematics
Problem
The functions
P
(
x
)
=
−
cos
x
+
2
P(x)=-\cos x+2
P
(
x
)
=
−
cos
x
+
2
and
Q
(
x
)
=
1
−
cos
x
−
4
Q(x)=1-\cos x-4
Q
(
x
)
=
1
−
cos
x
−
4
are antiderivatives of
sin
x
\sin x
sin
x
on
R
\mathbb R
R
. Find the constant
k
k
k
such that
Q
(
x
)
=
P
(
x
)
+
k
Q(x)=P(x)+k
Q
(
x
)
=
P
(
x
)
+
k
for all real
x
x
x
.
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