Chapter 9.2, Problem 7P

Write and solve the Euler equations to make the following integrals stationary. In solving the Euler equations, the integrals in Chapter 5, Section 1, may be useful.

${\displaystyle {\int }_{x_1}^{x_2}{e}^x}\sqrt{1+y^{\prime 2}}dx$

Hint: In the last integration, let $u=e^x$ and see Chapter 5, Problem 1.6