JEE Advanced | 2015Math miscellaneousHard
Question
The option(s) with the values of a and L that satisfy the following equation is(are)
= L ?
= L ?Options
A.a = 2, L = 
B.a = 2, L = 
C.a = 4, L =
D.a = 4, L =
Solution
Let I1 = 
(sin4 at cos4 at) dt
=
(sin6 at + cos4 at) dt + 
(sin6 at + cos4 at) dt
+
(sin6 at + cos4 at) dt + 
(sin6 at + cos4 at) dt
∴ I1 =
(sin6 at + cos4 at) dt + 
eπ+t (sin6 at + cos4 at) dt
+
e2π+t (sin6 at + cos4 at) dt + 
et+3π (sin6 at + cos4 at) dt
= (1 + eπ + e2π + e3π)
(sin6 at + cos4 at) dt
∴
= 1 + eπ + e2π + e3π = 
(sin4 at cos4 at) dt =
(sin6 at + cos4 at) dt + (sin6 at + cos4 at) dt+
(sin6 at + cos4 at) dt + (sin6 at + cos4 at) dt∴ I1 =
(sin6 at + cos4 at) dt + eπ+t (sin6 at + cos4 at) dt+
e2π+t (sin6 at + cos4 at) dt + et+3π (sin6 at + cos4 at) dt= (1 + eπ + e2π + e3π)
(sin6 at + cos4 at) dt∴
= 1 + eπ + e2π + e3π = Create a free account to view solution
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