Question

do number 2 please

1720 Submissions Used MY NOTES Evaluate the integral by making an appropriate change of variables. 9 COS dA where R is the trapezoidal region with vertices (4,0), (7,0), (0,7), and (0,4) + x 13 13 sin(3) X Need Help? Read It Watch It Talk to a Tutor Show My Work (Optional) 3. [0/1 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 13.2.001. 3/20 Submissions Used MY NOT Evaluate the line integral, where C is the given curve. y3ds, C: * = 4, y = t, Osts 5 7814.564 x Need Help? Read It Watch It Talk to a Tutor

Answer 1

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(2)

+4(0,7) 3 2 O-4 1 (4,0) 0-7 Low A = x tuto =) U = 2X+V :-) Griven. ssa cos (3 (4* x)) A verties (4,0), (7,0),(0,7) and (0,4) Finding line segment goining the points p4 (4,0to (0,4) 4-0= 4-0 (-4) ->x Tity's 6-(2,0) 9= -(8-4) =) 9 =-x+y (x+y=4 kine segment joining the points (1,0) to (0,7) 470= 1-0 (2-1) =) y =-|(x-7) =) x+y= The lire segment joining points (4,0) and (7,07;3 (4=0 The line segment joining points (6,4) and (0,7), 110 : The tetrahedron is bounded by the foureans. x=0; Y=0; x+y=4 ; x+y=1 regions in the uv-plane Corresponding to R Ytty ; v=y- - n=uay NOW Y = 4-0-y => V +0 = 24 5344= {(utv) 4- V+ substitutez oko x = 2 (uru) por NEU =) oc* (u-v) =) (UEV substitute yaoin 4=_CU +u => 07Ź (u tv) =) UFVEO =) V=-u so

aty - 4 and 244 = 7 { (0-1) ++ [+V)= 4 1/2 u + 2 U-4 ¿(u-u)+{(utv)=4 10+1057 I'U=4 U=' The limits of u varies from it to 7 and The units of u varies from -u.to.lu 1 میں کہا : (۷) } Now Partially The region of s Can be Expressed as S- 7, ususu} differentiate x and a wovito u andu d = Ž CU-v) and y= £ (utv) Du te = 1 = 24 ol Ox DV - 1 / 1 2 ЭЧ DV = 1 / 2 Let &=x(6,u) and y = 4 (0,4) then the Jacobe an of the transformation, I J(UV) = (19) (av) it 11 2x Du ou 29. Du ov = 44 tt M- Jw,v.) = 12 1 2 ½ . Change of variables in doubles integralis . If acos (3 (4- )) DA R Esfa cos Bolivar IS +(2,4)-d4 = 34f (o (Usv), ucu, poverty z

s u=4 V-u nu Sinay 74 9 ola 3 -u 3 - fa.cos) du.de cos(3) duidu :: (sio (34) [ussintu - siete } } ((sin3 +sin3)du - 3 5'6(251033).de, -3$ing) Surdu = 3 Sin3 [] = 3 sín 3 [ 32 so cu q - 1 =351n3 (12-1 = 3 sin3 = 99 sio3 2 :. The evaluated integralis 99 (sin3) 2