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Byju's Answer
Standard XII
Mathematics
Second Fundamental Theorem of Calculus
∫0π/2cos 2 x ...
Question
∫
π
2
0
c
o
s
2
x
d
x
=
A
1
−
π
4
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B
1
+
π
4
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C
π
4
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D
π
2
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Solution
The correct option is
C
π
4
Using gamma function,
∫
π
2
0
c
o
s
2
x
d
x
=
r
(
3
2
)
r
(
1
2
)
2
r
(
2
)
=
1
2
r
(
1
2
)
r
(
1
2
)
2.1.
r
(
1
)
=
π
4
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0
Similar questions
Q.
∫
π
4
0
t
a
n
2
x
d
x
=
Q.
∫
π
/
2
0
l
o
g
(
t
a
n
x
)
d
x
=
Q.
∫
0
π
/
2
x
sin
x
d
x
is equal to
(a) π/4
(b) π/2
(c) π
(d) 1
Q.
∫
π
4
0
t
a
n
2
x
d
x
=
[Roorkee 1983, Pb. CET 2000]