$\int_a^b \sqrt{(x'(t))^2 + (y'(t))^2} dt$

$\int_a^b (x'(t) + y'(t)) dt$

$\int_a^b \sqrt{1 + (y'(t))^2} dt$

$\pi \int_a^b (x(t)y'(t)) dt$