Evaluate SI ez?+y? dA where R is the upper half portion of the unit circle. R
3. (1.5 points) Evaluate the integral using a change of variables. (x + y)ez?-y dA JJR where R is the polygon with vertices (1,0), (0, 1), (-1,0), and (0, -1).
3. Evaluate the integral by changing to polar coordinates: SS (x+y) da R Where R is the region in quadrant 2 above the line y=-x and inside the circle x2 + y2 = 2.
Evaluate the given integral by changing to polar coordinates. ∫∫R(4x − y) dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x.
3 attempts left Check my work Evaluate J. (2++y+8) + y2 + 8) da, where R is the circle of radius 4 centered at the origin. The answer is C R
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z. 1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
7. Evaluate the following integral by converting to polar coordinates: S], 127 (2x – y)dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. 8. Find the surface area of the portion of the plane 3x + 2y +z = 6 that lies in the first octant. 9. Use Lagrange multipliers to maximize and minimize f(x, y) = 3x + y...
The force acting at a point (x, y) in a coordinate plane is F(x, y)- r-xit yj. Calculate the work done by E along the upper half of the circle x2 ya from (a, 0) to (-a, 0). where Irl The force acting at a point (x, y) in a coordinate plane is F(x, y)- r-xit yj. Calculate the work done by E along the upper half of the circle x2 ya from (a, 0) to (-a, 0). where Irl
(10) (8 points) Evaluate the line integral Scry ds, where C is the upper half of the circle r2 + y2 = 4.
Q4: Use polar coordinates to evaluate x2 - y2 dA, where R is the region in the first V9- quadrant within the circle x2 + y2-9.
QUESTION 4 Use the appropriate transformation to evaluate SX (2x + y)(x - y)dA where R is the region bounded by the line y = 4 - 2x, y = 7 - 2x, y = x - 2 and y = x +1. (8 marks)