Find the average value of f over the given rectangle. f(x,y) =4x2y, R has vertices (-2,0),(-2,5),(2,5),(2,0).
Find the average value of f over the given rectangle. f(x, y) = 2x2y, R has vertices (-5, 0), (-5, 4), (5, 4), (5,0). fave = _______
(1 point) Find the average value of f(x,y) = 2x + ey over the rectangle R = [0,5] x [0,7]. Average value =
Find the average value of f(x, y) over the region Rwhere A is the area of R in the following equation. Average value - Ā J 1(x,y) dA f(x,y) = xy R: rectangle with vertices (0, 0), (7,0), (1, 2), (0, 2) Enter a number Submit Answer Practice Another Version
Let F(x, y) = ( – 7x, 5y) and let R be the rectangle with vertices (0,0), (5,0), (0,3), and (5,3). Compute the flux of F across the rectangle. Begin by parameterizing each side of rectangle (oriented counterclockwise), and then compute the flux integral over each side individually. Preview
(1 point) Let R be the rectangle with vertices (0,0). (8,0). (8, 8), and (0,8) and let f(x, y)- /0.25ry. (a) Find reasonable upper and lower bounds for JR f dA without subdividing R. upper bound lower bound (b) Estimate JRf dA three ways: by partitioning R into four subrectangles and evaluating f at its maximum and minimum values on each subrectangle, and then by considering the average of these (over and under) estimates overestimate: Inf dA underestimate: JRfdA average:...
Find the average value of the function f over the given region. f(x,y) = 8x + 10y over the triangle with vertices (0,0). (10,0), and (0.6). O A. 30 OB. 80 3 OC. 140 3 OD. 86 3
Find the volume beneath z = f(x,y) and above the region described by the rectangle with vertices (0,0), (2,0), (2,3), and (0,3). f(x,y)=4x^2+9y^2 Hint: compute the double integral required to find the volume under f(x,y) using the limits of integration given by the region on the x-y plane.
Find the average value of the function over the given solid. The average value of a continuous function F(x, y, z) over a solid region is [/flx, y, z) ov where Vis the volume of the solid region Q. f(x, y, z) = x + y + z over the tetrahedron in the first octant with vertices (0, 0, 0), (5, 0, 0), (0,5, 0) and (0, 0, 5) 468/125 x
Let X and Y have a density, f, that is uniform over the interior of the triangle with vertices at (0,0), (2,0), and (1,2). Find the conditional expectation of Y given X.
Find the derivative of f(x, y, z) = (-4x2y, e-4y+32). f'(x, y, z) =