Mathematics for Economists

Homework

Find the general solution of the EulerñLagrange equation of the

functional

Zb

a



x

 2

t^3

dt

wherea> 0.

Find the general solution of the EulerñLagrange equation of the

functionals

Zb

a

p

t

r

1 +



x

 2

dt

Zb

a

t

r

1 +



x

 2

dt

Find the extremal solutions

Z 3

2

x^2



1 x

 2

dx, x( 2 )= 1 ,x( 3 )=

p

3.