Question

In Convert to cylindrical coordinates ſyddy Set up the integral) 1b. Convert to spherical coordinates JJ Jy daddy (Set up the integral) 2. Une cylindrical coordinates to determine the volume of the solid in the 1" octant enclosed by the coordinate planes, the cylinder + 16 and the plane (Set up - do not solve) 3. Use spherical coordinates to determine the volume of the solid that is bounded above by x + y + = 25 and below by : = x + y (set up-do not solve) 4. Evalute the given integral by using a transformation: J), 4(x + 2y)(x - y)'d where R is the region bounded by y = x.x=0&y=1 5. Given F(x,y) = (3xy)i +(2x-y)). Sketch 3 vectors in the vector field corresponding to the points (0.1). ( 1. 1) and (-1.1) 5b. Determine the div F and curl Fat (0.2.1): F(x,y. ) = (2)-(3x'vz)/ + 4zk! 6. Evaluate the line integral: fl y dsover OSISI Given C is the vector valued function r(t) = 21 + (e?) 7. Evaluate the line integral of F(x,y) = 31+ (2y) along the line segment that runs from (1,2) to (3,6). 8a. Evaluate: Oxydx +(2 ydy where is the boundary of the region lying between yox and x2 and v = 0 (counterclockwise orientation) Bb. Evaluate the integral in part b using Green's theorem

solve problem 6

it is not a double integral, it is 1 integral

Answer 1

xTyds r(t) = alt patj Ostel ř (t)- 0 + 20 2t Irl= 2e2t so x ryds = T (2) 3 /e at 11 ritill dt Is et qe atat = 16 let dat 16 e 3 + 10 = 10 (6-1).