The exact length of the parametric curve $x = e ^ { t } \cos t , y = e ^ { t } \sin t , 0 \leq t \leq \frac { \pi } { 7 }$ is $\sqrt { 2 } e ^ { x / 7 }$.

Question

Quizplus · Accepted Answer

The length of a parametric curve is calculated using the integral of the square root of the sum of the squares of the derivatives of x and y with respect to t. The given expression $\sqrt{2} e^{x/7}$ does not match the correct formula for the length of this curve.

The Exact Length of the Parametric Curve x=etcos⁡t,y=etsin⁡t,0≤t≤π7x = e ^ { t } \cos t , y = e ^ { t } \sin t , 0 \leq t \leq \frac { \pi } { 7 }x=etcost,y=etsint,0≤t≤7π​

The Exact Length of the Parametric Curve $x = e ^ { t } \cos t , y = e ^ { t } \sin t , 0 \leq t \leq \frac { \pi } { 7 }$