Chapter 8.5, Problem 2QQ

To determine

To find the length of the curve $x=\frac{t^4}{4};y=t^3$ from $t=0\text{to}t=2$ .

Answer to Problem 2QQ

Option(D).

Explanation of Solution

Given information: The curve $x=\frac{t^4}{4};y=t^3$ from $t=0\text{to}t=2$

Formula used: The length of the parametric curve is ${\displaystyle \underset{a}{\overset{b}{\int }}\sqrt{{x^{\prime }}^2+{y^{\prime }}^2}dt}$

Calculation :

The length of the curve is:

  $x^{\prime }=t^3;y^{\prime }=3t^2$

The length of the parametric curve is ${\displaystyle \underset{0}{\overset{2}{\int }}\sqrt{t^6+9t^4}dt}$ .