Tardigrade
Tardigrade - CET NEET JEE Exam App
Exams
Login
Signup
Tardigrade
Question
Mathematics
If n (2 n +1) ∫ limits01(1- x n )2 n dx =1177 ∫ limits01(1- x n )2 n +1 dx text , then n ∈ N is equal to
Q. If
n
(
2
n
+
1
)
0
∫
1
(
1
−
x
n
)
2
n
d
x
=
1177
0
∫
1
(
1
−
x
n
)
2
n
+
1
d
x
,
then
n
∈
N
is equal to _____
2446
128
JEE Main
JEE Main 2022
Integrals
Report Error
Answer:
24
Solution:
Let
I
1
=
0
∫
1
(
1
−
x
n
)
2
n
d
x
,
I
2
=
0
∫
1
(
1
−
x
n
)
2
n
+
1
d
x
I
2
=
0
∫
1
(
1
−
x
n
)
2
n
+
1
⋅
1
d
x
=
(
1
−
x
n
)
2
n
+
1
⋅
x
∣
∣
0
1
−
0
∫
1
(
2
n
+
1
)
(
1
−
x
n
)
2
n
(
−
n
x
n
−
1
)
x
d
x
I
2
=
−
n
(
2
n
+
1
)
{
I
2
−
I
1
}
(
2
n
2
+
n
+
1
)
I
2
=
n
(
2
n
+
1
)
I
1
I
2
I
1
=
n
(
2
n
+
1
)
2
n
2
+
n
+
1
=
n
(
2
n
+
1
)
1177
⇒
2
n
2
+
n
−
1176
=
0
⇒
n
=
24