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Suppose and . If is an arbitrary constant of integration then which of the following…
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
Suppose
J
=
∫
sin
2
x
+
sin
x
1
+
sin
x
+
cos
x
d
x
J = \int \frac{\sin^2 x + \sin x}{1 + \sin x + \cos x}\,dx
J
=
∫
1
+
s
i
n
x
+
c
o
s
x
s
i
n
2
x
+
s
i
n
x
d
x
and
K
=
∫
cos
2
x
+
cos
x
1
+
sin
x
+
cos
x
d
x
K = \int \frac{\cos^2 x + \cos x}{1 + \sin x + \cos x}\,dx
K
=
∫
1
+
s
i
n
x
+
c
o
s
x
c
o
s
2
x
+
c
o
s
x
d
x
. If
C
C
C
is an arbitrary constant of integration then which of the following is/are correct? (a)
J
=
1
2
(
x
−
sin
x
+
cos
x
)
+
C
J = \frac{1}{2}(x - \sin x + \cos x) + C
J
=
2
1
(
x
−
sin
x
+
cos
x
)
+
C
(b)
J
=
K
−
(
sin
x
+
cos
x
)
+
C
J = K - (\sin x + \cos x) + C
J
=
K
−
(
sin
x
+
cos
x
)
+
C
(c)
J
=
x
−
K
+
C
J = x - K + C
J
=
x
−
K
+
C
(d)
K
=
1
2
(
x
−
sin
x
+
cos
x
)
+
C
K = \frac{1}{2}(x - \sin x + \cos x) + C
K
=
2
1
(
x
−
sin
x
+
cos
x
)
+
C
Related theory
Antiderivatives
Trigonometric Identities
Trigonometric Functions
Standard trigonometric integrals
Integration using trigonometric identities
Integrals
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