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JEE Main Math Class 12 Integrals Part 4 Questions
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© examsnet.com
Question : 7
Total: 51
If
f
(
t
)
=
π
∫
0
2
x
dx
1
−
cos
2
t
s
i
n
2
x
,
0
<
t
<
π
, then the value of
π
2
∫
0
π
2
dt
f
(
t
)
equals ______.
[5 Apr 2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
f
(
t
)
=
π
∫
0
2
x
1
−
cos
2
t
s
i
n
2
x
dx
. . . (1)
=
2
π
∫
0
(
π
−
x
)
dx
1
−
cos
2
s
i
n
2
x
. . . (2)
2
f
(
t
)
=
2
π
∫
0
π
1
−
cos
2
t
s
i
n
2
x
dx
f
(
t
)
=
π
∫
0
π
1
−
cos
2
t
s
i
n
2
x
dx
divide & by
cos
2
x
f
(
t
)
=
π
π
∫
0
s
e
c
2
x
dx
s
e
c
2
x
−
cos
2
t
tan
2
x
f
(
t
)
=
2
π
π
∕
2
∫
0
s
e
c
2
x
dx
s
e
c
2
x
−
cos
2
t
tan
2
x
tan
x
=
z
s
e
c
2
x
dx
=
d
z
f
(
t
)
=
2
π
∞
∫
0
d
z
1
+
s
i
n
2
t
⋅
z
2
=
π
2
s
i
n
t
Then
π
∕
2
∫
0
π
2
f
(
t
)
dt
=
π
∕
2
∫
0
s
i
n
t
dt
=
1
© examsnet.com
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