Tardigrade
Tardigrade - CET NEET JEE Exam App
Exams
Login
Signup
Tardigrade
Question
Mathematics
Let α ∈(0,1) and β= log e(1-α). Let Pn(x)=x+(x2/2)+(x3/3)+ ldots+(xn/n), x ∈(0,1). Then the integral ∫ limits0α (t50/1-t) d t is equal to
Q. Let
α
∈
(
0
,
1
)
and
β
=
lo
g
e
(
1
−
α
)
. Let
P
n
(
x
)
=
x
+
2
x
2
+
3
x
3
+
…
+
n
x
n
,
x
∈
(
0
,
1
)
. Then the integral
0
∫
α
1
−
t
t
50
d
t
is equal to
1297
127
JEE Main
JEE Main 2023
Integrals
Report Error
A
P
50
(
α
)
−
β
0%
B
−
(
β
+
P
50
(
α
)
)
50%
C
β
+
P
50
(
a
)
0%
D
β
−
P
50
(
α
)
50%
Solution:
0
∫
α
1
−
t
t
50
−
1
+
1
=
−
0
∫
α
(
1
+
t
+
…
..
+
t
49
)
+
0
∫
α
1
−
t
1
d
t
=
−
(
50
α
50
+
49
α
49
+
…
..
+
1
α
1
)
+
(
−
1
l
n
(
1
−
f
)
)
0
α
=
−
P
50
(
α
)
−
ln
(
1
−
α
)
=
−
P
50
(
α
)
−
β