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Standard XII
Mathematics
Question
If
∫
π
/
3
0
cos
x
3
+
4
sin
x
d
x
=
k
log
(
3
+
2
√
3
3
)
, then
k
is equal to
1
2
1
3
1
4
1
8
A
1
2
B
1
3
C
1
4
D
1
8
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Solution
Verified by Toppr
∫
π
/
3
0
cos
x
3
+
4
sin
x
d
x
Let
z
=
3
+
4
sin
x
⟹
d
z
=
4
cos
x
d
x
⟹
cos
x
d
x
=
d
z
4
When
x
=
0
,
z
=
3
and when
x
=
π
3
,
z
=
3
+
2
√
3
Hence, integration becomes:-
1
4
∫
3
+
2
√
3
3
1
z
d
z
=
1
4
[
log
z
]
3
+
2
√
3
3
=
1
4
log
(
3
+
2
√
3
3
)
⟹
k
=
1
4
Hence, answer is option-(C).
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