2. (2 points) Use the midpoint rule to estimate (7 – 2x – y)dA over the...
Use the Midpoint Rule for the triple integral to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.) dV, where III 1.4 + se't sy + r1 = {(x, y, z)|0 5 x 5 4,0 5 7 5 8,0 5 254} B =
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)
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...
EXAMPLE 5 Use the Midpoint Rule with n = 5 to approximate the following integral. dx х SOLUTION The endpoints of the subintervals are 1, 1.6, 2.2, 2.8, 3.4, and 4, so the midpoints are 1.3, 1.9, 2.5, 3.1, and width of the subintervals is Ax = (4 - 175 so the Midpoint Rule gives The 1.9* 2s 313) dx Ax[f(1.3) + (1.9) + (2.5) + F(3.1) + f(3.7)] -0.06 2 + 1.3 2.5 3.1 . (Round your answer to...
Evaluate: vr y-x dA , y + 2x+1 where R is the parallelogram bounded by y-x-2, y-x-3, y + 2x = 0, andy+2x=4. Evaluate: vr y-x dA , y + 2x+1 where R is the parallelogram bounded by y-x-2, y-x-3, y + 2x = 0, andy+2x=4.
(-2<x<3 21 Graph the feasible region for the system-15y 35 (2x + y<6
Use the Midpoint Rule with n = 5 to approximate the area of the region bounded by the graph of f and the x-axis over the interval. (Round your answer to two decimal places.) 13. [-75.55 Points] DETAILS LARAPCALC10 5.6.012. MY NOTES Use the Midpoint Rule with n = 5 to approximate the area of the region bounded by the graph of f and the x-axis over the interval. (Round your answer to two decimal places.) Function Interval f(x) =...
12. Let R ((x, y)l0 s r s 4,0 s y s 6). Let f(x, y)2+2y Express the Riemann sum estimate for Jjf(x, y)dA with m 2,n 3 using both summation notation and expanded sum form if the sample points are the upper right corners of each sub-rectangle. Do not evaluate. 12. Let R ((x, y)l0 s r s 4,0 s y s 6). Let f(x, y)2+2y Express the Riemann sum estimate for Jjf(x, y)dA with m 2,n 3 using...
(15 pts) Find (2x - y) dA, where R is the triangular region with vertices (0,0), (1, 1), and (2, -1). Use the change of variables u = x - y and v = x + 2y.
Using Change of Variables..Evaluate ∫∫ R 15y/x dA where R is the region bounded by xy = 2, xy = 6 , y = 4 and y =10 usingthe transformation x=v , y=2u/3v.