Question

Find the work done by the force field F on a particle that moves along the curve C.

    F(x,y)=xy  i+x^2  j
 C: x=y2 from (0,0) to (4,2)

Enter the exact answer as an improper fraction, if necessary.

W=

Answer 1

the Curve On а + • It is asked to find the work done by the force field Paxy + x² j on the particle theet moves along C: 2=y? from (0,0) to Chia) Nete] The work done by a parce field particle moning along C, which is parameteuäed as 7 = 8(t) from t= 4, to t=t, es ginen by the line integral Mosh, W = ( F. do - Sportled at F (act)) }(6) at Curne tz tz iti

dets parameterize the wine C: x=y² from (0,0) to (4, 2) as fellenes og zit gi 2 y=t x=y²=t 7 (t) = t² i + tj y = t yo » when when t=0 t=2 y =) ostaa 3'6)=0[t’i + tj] – at itu FH)), the +421 at tit th j i flăct)).'t) = (43i++"g").Cat i+j) ح

at t² + + x1 = 8th rocha 3th at ..We 2 Note ) Saranx= ahhh te t=o 5 2 na- 3.t 5 (19-05)=*32 - 96 W = 96 5