please see the attachment.
evaluate JJ. (< –Y) A. ) Integrate f(x, y, z) = x2 + y2 + 22 over the cylinder x2 + y2 < 2,-2 <2<3 (IL dx dy dz Feraluate
#1: Use a change of variables to integrate f (x, y) = y - x over the region described by: –3 <y – 2x < 0 and 0 < 2y – x < 3.
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29 8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
(1 point) y2 and below the paraboloid 8xz over the region in the first octant(x, y, z 0) above the parabolic cylinder z Integrate f(x, y, z) Answer: (1 point) y2 and below the paraboloid 8xz over the region in the first octant(x, y, z 0) above the parabolic cylinder z Integrate f(x, y, z) Answer:
10) Integrate W =./x2 +y2+22 e tr+vrj in the region given by the set 11) Is the following vector field F conservative, compressible and rotational? F(asino) Fx, y 2Esnsn) 10) Integrate W =./x2 +y2+22 e tr+vrj in the region given by the set 11) Is the following vector field F conservative, compressible and rotational? F(asino) Fx, y 2Esnsn)
Integrate f(x,y)=x2 + y over the triangular region with vertices (0,0), (1,0), and (0,1). The value is (Type a simplified fraction.)
2. Let R be the region R = {(X,Y)|X2 + y2 < 2} and let (X,Y) be a pair of random variables that is distributed uniformly on this region. That is fx,y(x, y) is constant in this region and 0 elsewhere. State the sample space and find the probability that the random variable x2 + y2 is less than 1, P[X2 +Y? < 1].
For f(x, y) = k(x2 + y2), 0<x< 1 and 0 <y<1 and 0 elsewhere: a) Find k. b) Are X and Y independent? c) Find P(X<0.5, Y>0.5), P( X = 0.5, Y>0.5).
Let f(x, y) = x2 – yż and D= {(2,y) : x2 + y2 < 4}. Let m and M be the absolute minimum and maximum values of f over D respectively. What is m - M?
Triple Integration Problems. 1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders x2 + y2 4 and x2 + y,: 9 = x+9+ 3 and by the 2. Integrate where E is bounded by the zu-plane and the hemispheres z/9-2y2 and z = V/10-22-27 Change the order of integration and evaluate x3 sin(уз)dydx. 0 Jr2 1. Integrate zdV JJ w where ll' is enclosed by the planes z = 0 and cylinders...