Integral of Exponential Function (Jee Mains) | ExamDuo
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Definite Integrals and Reduction
Medium
Integral of Exponential Function
Let
f
:
ℝ
→
ℝ
be a function defined by
f
(
x
)
=
4
x
4
x
+
2
and
M
=
f
(
1
−
a
)
∫
f
(
a
)
x
s
i
n
4
(
x
(
1
−
x
)
)
dx
N
=
f
(
1
−
a
)
∫
f
(
a
)
s
i
n
4
(
x
(
1
−
x
)
)
dx
;
a
≠
1
2
.
If
α
M
=
β
N
,
α
,
β
∈
ℕ
, then the least value of
α
2
+
β
2
is equal to
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