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Byju's Answer
Standard XII
Mathematics
First Fundamental Theorem of Calculus
∫ x cos 3x2 s...
Question
∫
x
cos
3
(
x
2
)
sin
(
x
2
)
d
x
is equal to
A
−
cos
4
(
x
2
)
sin
(
x
2
)
16
+
C
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B
cos
(
x
2
)
16
+
C
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C
−
cos
4
(
x
2
)
8
+
C
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D
cos
3
(
x
4
)
8
+
C
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Solution
The correct option is
C
−
cos
4
(
x
2
)
8
+
C
∫
x
cos
3
(
x
2
)
sin
(
x
2
)
d
x
Let
x
2
=
t
⇒
2
x
d
x
=
d
t
=
1
2
∫
cos
3
(
t
)
sin
(
t
)
d
t
Let
cos
t
=
z
⇒
−
sin
t
d
t
=
d
z
=
−
1
2
∫
z
3
d
x
=
−
z
4
8
+
c
1
=
−
cos
4
(
x
2
)
8
+
C
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