Webthen y=0,4. x 2=4y. we get x=4,0. So, the points of intersection are (0,0) & (4,4) Area =∫04∫ 2 xx 2/4dydx=∫04[y] 2 xx 2/4dx. =∫04[ 4x 2−2 x]dx. =[12x 3− 34⋅x 3/2]04. =[124 3− 34(4) 3/2] = 316 sq. units. WebQuestion: (1 point) Consider the vector field F(x,y,z)=(4z+4y)i+(5z+4x)j+(5y+4x)kF(x,y,z)=(4z+4y)i+(5z+4x)j+(5y+4x)k. a) Find a function ff such that F=∇fF=∇f and f(0,0,0)=0f(0,0,0)=0. f(x,y,z)=f(x,y,z)= b) Suppose C is any curve from (0,0,0)(0,0,0) to (1,1,1).(1,1,1). Use part a) to compute the line integral ∫CF⋅dr∫CF⋅dr.
Answered: Let R be the region bounded by the… bartleby
WebQ1 (14 points) Let R be the region bounded by the curves C1: y=-4x + 2.2 + 2 and C2:y= -2x + 2? +2. C2 C1 A B B a) [3.5 points] Find the coordinates of the intersection points A and B. b) [5 points) Find the area of R. C) [2.5 points] Set up a definite integral for the volume of the solid obtained by rotating R about the line y = 5. WebOct 19, 2024 · Q2. [2 points] Let R be the region bounded between the curves y = x 2 and y = 12 − x 2. Let S be ... 9 + y 2 ∆y. (b) [2 points] Again, consider a thin horizontal strip of this door, of thickness ∆y m, and located about y m from the bottom of the tank. ... y 2. dy = ∫. 2 x 4 x 2 + 10. dx u = 4x 2 + 10 =⇒ du = 8x dx creative jobs in houston
Consider the two curves C1 : y^2 = 4x, C2: x^2 + y^2 - 6x + 1
WebTranscribed Image Text: Let R be the region bounded by the curves C1 : y – 3 = -2(x – 1), C2 : x+ y = 4, and C3 : y = 1. y (1,3) (0,1) (3,1) Set up (but do not evaluate) a definite integral or sum of definite integrals that is equal to the following. a. Area of R using vertical rectangles b. Length of the boundary of R along C1 c. Volume of the solid generated … Web16.2 Line Integrals. We have so far integrated "over'' intervals, areas, and volumes with single, double, and triple integrals. We now investigate integration over or "along'' a curve—"line integrals'' are really "curve … WebQuestion Consider the two curves C 1:y 2=4x C 2:x 2+y 2−6x+1=0 Then, the area of region between these curves? A 320−2π B 310−2π C 320−π D 310−π Hard Solution … creative jobs in advertising example