xy? Find Slip -dA, R= [0, 3] x [ – 4,4 R x2 + 1
(1 point) Solve the system 3 9 da dt 2 -1 -3 2 with x(0) 4 Give your solution in real form. 21 = 22 =
Evaluate: vr y-x dA , y + 2x+1 where R is the parallelogram bounded by y-x-2, y-x-3, y + 2x = 0, andy+2x=4.
Evaluate: vr y-x dA , y + 2x+1 where R is the parallelogram bounded by y-x-2, y-x-3, y + 2x = 0, andy+2x=4.
dA, where R is the trapezoidal region cos yt x with vertices (1,0), (2, 0), (0,2), and (0, 1)
dA, where R is the trapezoidal region cos yt x with vertices (1,0), (2, 0), (0,2), and (0, 1)
1. Evaluate x+1 using Mathematica. I. (4+1+y)d4; R DA; R = {(x,y): 0 5xs1, 2s y s3} and check your answer
1. Evaluate S SR(5 – y)dA with R= {(x, y)|0 SX 55,0 Sy < 4} by identifying it as the volume of a solid and then calculating the volume geometrically.
Exercise 3 Approximate SS (y – x2 + 2)dA for R = [0, 2] [0, 3) using n = 4 subintervals in the R x-direction and m= 6 subintervals in the y-direction. Exercise 4 A volume of sediment is being measured in a geological survey. The depth of the sediment is measured every three meters in both directions and is given in meters in the following table. y 0 3 6 9 12 . 0 3 6 9 12 0123...
1/3 x + y 7. Consider dA where R is the region bounded by the triangle with vertices (0,0), (2,0), V= x+y X-y and (0,-2). The change of variables u=- defines a transformation T(x,y)=(u,v) from the xy-plane 2 to the uv-plane. (a) (10 pts) Write S (in terms of u and v) using set- builder notation, where T:R→S. Use T to help you sketch S in the uv-plane by evaluating T at the vertices. - 1 a(u,v) (b) (4 pts)...
Evaluate Double Integrals of sqrt(36 − x^2) dA, where R = [0, 6] × [−5, 4], using GEOMETRY only.
3. Define the function f : R2 + R by 1 if x > 0 f(x) = { -1 if x >0 10 otherwise. and and X < y < x + 1, +1 < y < X + 2, Show that [ f(x,y) (da) \(dy) + | | f(x,y) A(dy) A(da). Why is this not a contradiction to Fubini's Theorem?