Find the length of the curve.
-$$x = \int _ { y } ^ { 1 } \sqrt { t ^ { 3 } - 1 } d t , 1 \leq y \leq 9$$
A) $\frac { 484 } { 5 }$
B) 20
C) $\frac { 481 } { 5 }$
D) $\frac { 52 } { 3 }$

Question

Quizplus · Accepted Answer

The correct answer is A because the length of the curve is given by the integral of the square root of 1 plus the square of the derivative of x with respect to y.

Find the Length of the Curve x=∫y1t3−1dt,1≤y≤9x = \int _ { y } ^ { 1 } \sqrt { t ^ { 3 } - 1 } d t , 1 \leq y \leq 9x=∫y1​t3−1​dt,1≤y≤9

Find the Length of the Curve $x = \int _ { y } ^ { 1 } \sqrt { t ^ { 3 } - 1 } d t , 1 \leq y \leq 9$