Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
h
h
h
be continuous on
[
0
,
8
]
[0,8]
[
0
,
8
]
with
h
(
x
)
≥
0
h(x)\ge 0
h
(
x
)
≥
0
for
0
≤
x
≤
2
0\le x\le 2
0
≤
x
≤
2
and
6
≤
x
≤
8
6\le x\le 8
6
≤
x
≤
8
, while
h
(
x
)
≤
0
h(x)\le 0
h
(
x
)
≤
0
for
2
≤
x
≤
6
2\le x\le 6
2
≤
x
≤
6
. Given that
∫
0
8
h
(
x
)
d
x
=
−
3
\displaystyle\int_{0}^{8} h(x)\,dx=-3
∫
0
8
h
(
x
)
d
x
=
−
3
and
∣
∫
6
8
h
(
x
)
d
x
∣
=
1
\left|\int_{6}^{8} h(x)\,dx\right|=1
∫
6
8
h
(
x
)
d
x
=
1
, identify which integral has the greater absolute value:
∫
0
2
h
(
x
)
d
x
\displaystyle\int_{0}^{2} h(x)\,dx
∫
0
2
h
(
x
)
d
x
or
∫
2
6
h
(
x
)
d
x
\displaystyle\int_{2}^{6} h(x)\,dx
∫
2
6
h
(
x
)
d
x
.
Browse the problem library