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Find the antiderivative of cos x + sin x?
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Find the antiderivative of cos x + sin x?
asked
Sep 5, 2018
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Find the antiderivative of cos x + sin x?
Mathematics
high-school
Moha
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Moha
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1
Answer
6
votes
-1/4 cos 2x + C
or 1/2 sin^2 x + C
or -1/2 cos^2 x + C
well,
sinx
cosx
=
sin2
x
2
so you are looking at
12
∫
sin2
x
dx
=
(
12
)
[
(
12
)
(−
cos2
x)
+C]
=−
14
cos2
x+C'
or maybe easier you can notice the pattern that
(
sinn
x
)
'=n
sin
n−1
x
cosx
and pattern match. here
n−1=1
so n = 2 so we trial
(
sin2
x
)
'
which gives us
2
sinx
cosx
so we now that the anti deriv is
12
sin2
x
+C
the other pattern also works ie
(
cosn
x
)
'=n
cos
n−1
x
(−
sinx
)
=−n
cos
n−1
x
sinx
so trial solution
(−
cos2
x
)
'=−2
cosx
(−
sinx
)
=2
cosx
sinx
so the anti deriv is
−
12
cos2
x
+
C
Nij
answered
Sep 10, 2018
by
Nij
8.4k
points
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