Question

Provide a clear and organized presentation. Show all of your work. Present completely simplified exact answers only. Any solution that involves work that resembles that of integration by integration tables will immediately earn a zero

Evaluate AF F. dr using the fundamental theorem for line integrals, if Z -1 F(x, y, = { to tan z + ln xyz + 4x’y_z2 + 1 + x2' 2 1 tan y + 2x4yz2 + - y² + sec8 y tanº y, y 2 tantz+ via +2'g's +1+ - Z 1+ 22 and C is described by r(t) = (t – 43, 1, 1) over 44 <t < 45.

Answer 1

JE dr = Z c J <tantz + ln sy 2 + 40 3y²z²+ canly + 2x²yz ² + 9 = y² + see ytansy, C 1+22 tan'at r.-22 κ z + -z) 1+ 22 Ida, dy, dz) - s tan "2+ ln xyz +423 972 2 + 2 of 2) de +(tamly + 224 42²7 22 y 27 sec eytan yjdy C 2 +(tant at Z e-Z 2 zt VF22 It22 2/3 (45-44) + 45ln (45-43)– 44 10 (44-43)-S (t-43/+43 We have, 22 +22e4y²z+ + 2 +2x²y & + 2 + E-Z]dz 45 (tan'1 + (m1-43% +464-4333+ *-1,3,7) dt cirlt) =<7-43, 1,1).x=t-43, y=1, Z=1 dx=dt, dyzo.dt, dz=o.dt & 445+245 45 + lnlt-43) +464-43)*+ *2-13).-) at (3 47* [tlet-42) - sé de 14-43*7** + [tan"14-4397" bling integration by 45 +(45-43)4–84-4395) + tan" (45-43) - tank 44-43) +45162-0-L (1+43, 443) at +16-1 + tan'a-tan's 44 [* = sh 44 = 44 44 parts for fin (4-43) et 44 1) 44 t-43 d 45 klu 44

→ = JFdB = 4 +456m2 - [4+43m1t431], "s = 4512-[45+436145-431 – 44-4314144-431] +15+ tan2-7 4 44 +15+ tantz = 45.20 2. 2 1-43202 +15+tan'z = 211 2+14+tan's is F. dr 5/14 14+ 21n2+ zan 2 C