Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For a non-negative continuous function
f
(
x
)
f(x)
f
(
x
)
on
[
a
,
b
]
[a,b]
[
a
,
b
]
, the area of the region bounded by
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
, the
x
x
x
-axis, and the lines
x
=
a
x=a
x
=
a
and
x
=
b
x=b
x
=
b
is represented by a)
(
b
−
a
)
f
(
a
+
b
2
)
(b-a)\,f\!\left(\dfrac{a+b}{2}\right)
(
b
−
a
)
f
(
2
a
+
b
)
b)
∫
a
b
f
′
(
x
)
d
x
\displaystyle \int_a^b f'(x)\,dx
∫
a
b
f
′
(
x
)
d
x
c)
∫
b
a
f
(
x
)
d
x
\displaystyle \int_b^a f(x)\,dx
∫
b
a
f
(
x
)
d
x
d)
∫
a
b
f
(
x
)
d
x
\displaystyle \int_a^b f(x)\,dx
∫
a
b
f
(
x
)
d
x
Browse the problem library