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Manipal Entrance Test 2019 Math Paper
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© examsnet.com
Question : 68
Total: 70
If
I
n
=
∫
sin
n
x
d
x
,
then
n
I
n
−
(
n
−
1
)
I
n
−
2
equals
sin
n
−
1
x
cos
x
cos
n
−
1
x
sin
x
−
sin
n
−
1
x
cos
x
−
cos
n
−
1
x
sin
x
Validate
Solution:
(c) We know that, if
I
n
=
∫
sin
n
x
d
x
,
then
I
n
=
sin
n
−
1
x
cos
x
n
+
n
−
1
n
I
n
−
2
where
n
is a positive integer.
⇒
n
I
n
−
(
n
−
1
)
I
n
−
2
=
−
sin
n
−
1
x
cos
x
© examsnet.com
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