Understanding Engineering Mathematics

8.Determinedzfor the functions

(i) 2xdx− 6 ydy (ii) 6xy^3 dx+ 9 x^2 y^2 dy

(iii)

2 x

x^2 +y^2

dx+

2 y

x^2 +y^2

dy (iv) −sin(x+y)dx−sin(x+y)dy

(v) xe−xy(( 2 −xy)dx−x^2 dy)

dz

dt

=6cos2t+12 sin 2t−12 sint+4cost