Question

The length of the arc of the curve $6xy=x^4+3$ from $x=1,x=2$ is

• A. $\frac{13}{12}$ units
• B. $\frac{17}{12}$ units
• C. $\frac{19}{12}$ units
• D. $\frac{15}{12}$ units

Answer 1

Answer: (B)

$\frac{17}{12}$ units

Given curve is $y=\frac{x^4+3}{6x}=\frac{x^3}{6}+\frac{1}{2x}$

Differentiating w.r.t. $x$, we get
$y^{\prime }=\frac{x^2}{2}+\frac{-1}{2x^2}$
Length of Arc $={\int }_1^2\sqrt{1+(y^{\prime }{)}^2}dx$
$={\int }_1^2\frac{1}{2}(x^2+\frac{1}{x^2})dx$

$=\frac{1}{2}{[\frac{x^3}{3}-\frac{1}{x}]}_1^2$
$=\frac{17}{12}$