Calculate the following double integrals. Be sure to include a sketch of the region R. 1....
**All work must be shown to receive full credit.** Calculate the following double integrals. Be sure to include a sketch of the region R. no 121 2. (2xy)dydx given R={(x,y)0 SX S1x Sy s 1)
(5) Double Integrals M = } } Vå sin(x) dxdy 0 y2 (5a) Find the region Rover which we are integrating in the xy-plane. (5b) Rewrite the given integral in terms of dydx. (50) Evaluate this new integral to find the mass M of the planar region R.
:. (1o points) Sketch the following region, then set up double integrals that calculate the area of it. bound by y (x-2)2 and y. You do not have to integrate it
Let the region R be the triangle with vertices (1, 1), (1,3), (2, 2). Write the iterated integrals for SSR f(x, y)dA 1. in the “dydx” order of integration 2. in the “dxdy” order of integration
1. Evaluate the iterated integrals: x2+2x+y a. JR 3x+3y dA, R: 15x32,0 sys 1 (Hint: Simplify the integrand first.) b. S ey/*dA where R is the region in the xy-plane bounded between y = x2 and y = x over the interval 1sx52. c. So Sex Sx**2 x dydzdx
5.Use polar coordinates system to evaluate: x2 + y2)dydx , R is the region enclosed by 0 <x< 1 and, -x sy sx
Problem 4.(10 points.) Let a region R bounded by x – 3y = 0, x – 3y = 1, y = 0 and y=1. (a) (2 points) Sketch the region R. (b) (8 points) Compute Vy(x – 3y)dxdy
1. Sketch the region R of integration. Switch the order of integration and then integrate the problem. π x y cos x dy dx 0 0 2, Find the mass, the moments about the x- and y-axis, and the center of mass of the lamina bounded by the graphs of the given equations. Show a sketch of the region sensie Inx - dydx x
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a different set of l (b) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v F(u, u)dudu- F(u(x,y),o(x,y))dxdy coordinates for the Cartesian plane. Then (c) Let R denote a square of sidelength 2 defined by the inequalities |x-1, lul (3y,...
Thanks In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows: 0 f(x, y)dy dr f (r, y)dy d f(x, y) dA -2 2 TJ= Sketch the region and express the double integral integration as an iterated integral with reversed order of