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Question
Mathematics
If the integral In= displaystyle ∫ 0(π /2)(sin (2 n - 1) x/sin â¡ x)dx , then the value of [I20]3-[I19]3 is
Q. If the integral
I
n
=
∫
0
2
π
s
in
x
s
in
(
2
n
−
1
)
x
d
x
, then the value of
[
I
20
]
3
−
[
I
19
]
3
is
2039
187
NTA Abhyas
NTA Abhyas 2020
Integrals
Report Error
A
400
B
200
C
361
D
0
Solution:
I
20
−
I
19
=
∫
0
2
π
s
in
x
s
in
(
39
x
)
−
s
in
(
37
x
)
d
x
⇒
I
20
−
I
19
=
∫
0
2
π
s
in
x
2
s
in
x
cos
(
38
x
)
d
x
⇒
I
20
−
I
19
=
∫
0
2
π
2
cos
(
38
x
)
d
x
=
[
19
s
in
(
38
x
)
]
2
π
0
=
19
s
in
(
2
38
π
)
=
0
∴
I
20
=
I
19
Hence,
[
I
20
]
3
−
[
I
19
]
3
=
0