Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Calculate the arc length of the parabola
y
=
1
2
x
2
y=\dfrac{1}{2}x^{2}
y
=
2
1
x
2
from
x
=
0
x=0
x
=
0
to
x
=
1
x=1
x
=
1
. a)
1
2
(
2
+
ln
(
2
)
)
\dfrac{1}{2}\bigl(\sqrt{2}+\ln(\sqrt{2})\bigr)
2
1
(
2
+
ln
(
2
)
)
b)
1
2
(
2
+
ln
(
1
+
2
)
)
\dfrac{1}{2}\bigl(\sqrt{2}+\ln(1+\sqrt{2})\bigr)
2
1
(
2
+
ln
(
1
+
2
)
)
c)
2
+
ln
(
1
+
2
)
\sqrt{2}+\ln(1+\sqrt{2})
2
+
ln
(
1
+
2
)
d)
2
3
(
2
2
−
1
)
\dfrac{2}{3}\bigl(2\sqrt{2}-1\bigr)
3
2
(
2
2
−
1
)
Browse the problem library