Textbook Problem

Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the curve C in the x y-plane and under the surface $z=f\left(x,y\right)$, where

$\text{Lateral surface area}={\displaystyle {\int }_{C}f}(x,y)ds\cdot$.

$\begin{array}{cc}f\left(x,y\right)=xy,& C:y=1-x^2\end{array}$ from (1, 0) to (0, 1)