Problem 3
Find the extremuls of the following functionals: $$ \int_{x_{1}}^{x_{2}}\left(y^{2}+y^{2}+2 y^{x}\right) d x \text {. } $$
Problem 4
Find the extremuls of the following functionaln: $$ \int_{0}^{\pi / 2}\left(y^{2}+y^{2}-2 y \sin x\right) d x, y(0)=y(\pi / 2)=0 $$
Problem 7
Find the extremuls of the following functionaln: $$ \int_{1}^{2} \frac{x^{3}}{y^{2}} d x ; y(1)=0, y(2)=3 . $$
Problem 8
Find the extremuls of the following functionaln: $$ \int_{1}^{2} \frac{\sqrt{\left(1+y^{2}\right)}}{x} d x ; y(1)=0, y(2)=1 . $$
