Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
(
x
)
=
e
x
+
1
e
x
−
1
f(x) = \frac{e^x + 1}{e^x - 1}
f
(
x
)
=
e
x
−
1
e
x
+
1
and
∫
0
1
x
3
(
e
x
+
1
)
e
x
−
1
d
x
=
α
\int_{0}^{1} \frac{x^3(e^x + 1)}{e^x - 1} dx = \alpha
∫
0
1
e
x
−
1
x
3
(
e
x
+
1
)
d
x
=
α
. Then,
∫
−
1
1
t
3
f
(
t
)
d
t
\int_{-1}^{1} t^3 f(t) dt
∫
−
1
1
t
3
f
(
t
)
d
t
is equal to (1) 0 (2)
α
\alpha
α
(3)
2
α
2\alpha
2
α
(4)
α
2
\alpha^2
α
2
Browse the problem library