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Mathematics
Mathematics
Problem
Which integral represents the exact length of the graph of
y
=
x
3
y=x^{3}
y
=
x
3
on the interval
0
≤
x
≤
2
0\le x\le 2
0
≤
x
≤
2
? a)
∫
0
2
1
+
3
x
2
d
x
\displaystyle \int_{0}^{2}\sqrt{1+3x^{2}}\,dx
∫
0
2
1
+
3
x
2
d
x
b)
∫
0
2
(
1
+
9
x
4
)
d
x
\displaystyle \int_{0}^{2}\bigl(1+9x^{4}\bigr)\,dx
∫
0
2
(
1
+
9
x
4
)
d
x
c)
∫
0
2
1
+
(
3
x
2
)
2
d
x
\displaystyle \int_{0}^{2}\sqrt{1+(3x^{2})^{2}}\,dx
∫
0
2
1
+
(
3
x
2
)
2
d
x
d)
∫
0
2
1
+
(
x
3
)
2
d
x
\displaystyle \int_{0}^{2}\sqrt{1+(x^{3})^{2}}\,dx
∫
0
2
1
+
(
x
3
)
2
d
x
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