Mathematics

Problem

A wire is bent to follow the curve

y=x^{2}

for

0\le x\le 3

, with

x

measured in meters. Its linear density at a point with coordinate

x

\lambda(x)=2x

kilograms per meter. Which of the following gives the exact mass

M

of the wire? a)

\displaystyle \frac{37\sqrt{37}}{6}\text{ kg}

36\text{ kg}

\displaystyle \frac{37\sqrt{37}-1}{6}\text{ kg}

\displaystyle \frac{20\sqrt{10}-2}{3}\text{ kg}