sin y 11. Evaluate the integrals Sysin xy dxdy and sketch the corresponding 0 0 region....
(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.
1. Evaluate triple integrals. sinx sin y dzdydx (a)Jo So (b) o JoV dz dxdy
6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy. 6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy.
Sketch the region of the integral and evaluate the iterated integral: Slot V1 + x^dxdy.
To evaluate the following integrals carry out these steps. a. Sketch the original region of integration R in the xy-plane and the new region S in the uv-plane using the given change of variables. b. Find the limits of integration for the new integral with respect to u and v. c. Compute the Jacobian. d. Change variables and evaluate the new integral. х x,y): 0 5x57, 7 sys 6 - -x}; use x=7u, y = 6v - u. S5x25x+7y da,...
Calculate the following double integrals. Be sure to include a sketch of the region R. 1. . (2x + 3y)dxdy given R={(x,y)|0 SX < 2,1 sy s3} 2. SR (2xy)dydx given R={(x,y)|0 SX S1,x Sy s 1}
| -11 points LARCALCET7 14.2.010. Sketch the region and evaluate the terated integrat xY) de 6 8 10 //**.7-O
Evaluate the integral using a change of variables. Z ZR (x + y) sin(x − y) dA (Z's are integrals) where R is the triangular region with vertices (−1, 1), (1, 1), and (0, 0).
Evaluate the region of integration given by /4 cosy 6. x'siny dxdy Evaluate the region of integration given by /4 cosy 6. x'siny dxdy
question 2a) how to sketch the region -2y_y² g S S x3y dxdy Question 2 Sketch the region Rand evaluate the area (a) S'(1-4x+8y) dy dx SLPxydxdy 2