Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a differentiable function such that
f
′
(
x
)
+
f
(
x
)
=
∫
0
x
f
(
t
)
d
t
f'(x) + f(x) = \int_{0}^{x} f(t)\, dt
f
′
(
x
)
+
f
(
x
)
=
∫
0
x
f
(
t
)
d
t
. If
f
(
0
)
=
e
−
2
f(0) = e^{-2}
f
(
0
)
=
e
−
2
, then
2
f
(
0
)
−
f
(
2
)
2f(0) - f(2)
2
f
(
0
)
−
f
(
2
)
is equal to ________. [JEE MAINS - ONLINE - 2023]
Browse the problem library