Question

good evening.

i need help with this calculus question.

i will thumbs up your answer.

[25 pts) Let F(x, y, z) = (2xy + 2)i + (4x²y3 + 2yz)j + (5224 + 3y²z2)k and let C be the curve given parametrically by r(t) = (3t+1)i + tºj + 5tk for 0 <t<1. Evaluate the line integral [F. '. dr

Answer 1

and f(t) = (3t+1) itthj+5tr Given E=(ang²+ z3)i + (any +24835 +(5934+3932) k Compare F(x)= xit gj+ 3F 1 then a= 3t+ da=30t ob Izt, z=56 idy=2tar, dz25.dt Ē =CO(3t+1]2*3*+(505) + [4(3+++++2(+)(513) + s(34+0 (5+4+3(e)*sti] [(6t+2) €8 +3125-45] +[419++1+6t] ++250 € ] [('st+5) 626+7)+3Ct*) cast] =[64 +2+ +3125ť]T +[36+&+4+*+24+77.250€]T +(937575 +3125+*+7526 JK

If E=Filt F₂J + F F and dr= dalt dyJtd3E then E. dr = fi dat fz dy + fs de we have oi for given F.08= [6+'+2+ 84312575] 3.dt + [36+8+4+®+24+*+250t+J etdi + [9335.7673125+*+75+]sdr = tet + 6+84 321-1 Jd- +[72+ +8* +48+*+soot fit +[46875+ +15625€++385 = [90ť" t'+547° +84 +37576 +5675025 562579] Sēdf= j'[9044544°46+*+335 +5675045415625+*]d +15625 Where ostal dh t-o

8 어 54t 19 +8t +33stY [ion 54 다. 9 & ㅋ 56 ISO 97. + 15625X t 5 뷁 9 90 90ㅗ lo +54 48.1 35 + 1 8 t S6901 잉 T7SI (①)-[무, 6 5650 구 SOS ㅋ + 3125 +)+9+ b] = 6 2 SBS 314t 3 + 이 = 1 2 652. 1048