Chapter 8.5, Problem 1QQ

To determine

To find the equation of the curve which contains the point (1, 4).

Answer to Problem 1QQ

Option(A).

Explanation of Solution

Given information: The length of a curve ${\displaystyle \underset{0}{\overset{1}{\int }}\sqrt{1+16x^6}dx}$

Formula used: The length of a curve from $x=a\text{to}x=b$ is ${\displaystyle \underset{a}{\overset{b}{\int }}\sqrt{1+{\left(y^{\prime }(x)\right)}^2}dx}$

Calculation :

The point (1, 4) lies on the curve $y=x^4+3$