Problem:• an

⇐tie.

We paramehize

Elby

X=X , y=x2 * El

So ,2xds=Sj2xfEE= ¥ .3eH4xy÷f= 55¥

For a,

we parametriz by

x=l, y=y ⇐YEZ

fazx .ds=f2z. ftp.sizdy-2

Thus.

sex .ds= M¥+2 .

Problem # 2 .

a) Set 'dr= fist'

,

-

'

t'>.< stsztsdt

=fj(t'

. zt' ) .dt= To - at = 's -55=2+0

; F .dr= Soksint, cost , that,

- zt,

Ddt

= fo'

sntstdt - flustttdt + fjtdt

= 1- wsl - silt¥=f - Sil - wsl

B) .

Because awlttko ,it is conservative .

suppose

Fit

§ =2xyte32¥s=3ye3Z

⇒ fcxy ,⇒= jxthcy .)

⇒ zxyttfty =2xy+e32' ⇒ ¥y=ek⇒ t.ly#=e3?y+gcz)

⇒ fcxiy,z)=y2xte32ytgH⇒ 0§z= }ye3Z+jcz)=3ye32⇒

ojczto ⇒ gczkc

⇒

ftxifzky 'xt3ye34c .

-

I

1

1

and the field is defined on1123

,

which is simplyconnected .

v

.