Let F(x, y) = ( – 7x, 5y) and let R be the rectangle with vertices...
12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise. 12. (5 Points) Use Green's Theorem to evaluate the line integral dr +(7x + cos(y?)) dy, +5y where C is the path around the triangle with vertices (0,0), (4,0), (0,6), oriented counterclockwise.
(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:...
Let F(x,y,z) = <7x, 5y, 2z > be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 72 = 9 in the first octant. Answer: Finish attempt
Let F(x,y,z) = <7x, 5y, 2z> be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 7z = 8 in the first octant. Answer:
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.
Let F = (x,y) and C be the triangle with vertices (0,5) and (3,0) oriented counterclockwise. Evaluate 9. Fodr by parameterizing C. Use a parametric description of C and set up the integral. 1 $ F•dr=So dt 0 Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. of O A. For F = (f,g), evaluating the integral using дх дg and ду = results in a nonzero value of og OB. For...
4. Let ABCD be a rectangle with vertices A-(0,0), B 4,0) C(4,3), D (0,3) Suppose an isometry f: RR maps ABCD to a new rectangle PQRS where P-f(A)(2,4) and R- f(C)(2,9) Find all possible isometries f, and the remaining points Qf(B) and S-f(D) of the new rectangle.
1. Find the absolute maximum and minimum values of f(r,y) = x2+y2+5y on the disc {(x, y) | x2+y2 < 4}, and identify the points where these values are attained 2. Find the absolute maximum and minimum values of f(x, y) = x3 - 3x - y* + 12y on the closed region bounded by the quadrilateral with vertices at (0,0), (2,2), (2,3), (0,3), and identify the points where these values are attained. 3. A rectangular box is to have...
Evaluate the integral [c F.dr. F(x, y) = (x + y) i + (3x - cos y) j where is the boundary of the region that is inside the square with vertices (0,0), (4,0),(4,4), (0,4) but is outside the rectangle with vertices (1, 1), (3,1),(3,2), (1,2). Assume that C is oriented so that the region R is on the left when the boundary is traversed in the direction of its orientation.
6. (4 marks) Compute the line integral SF. dr, where F(x, y) = (x² + 10xy + y²,5x² + 5xy) and C is the boundary of the square with vertices (0,0), (0,2), (2,0), and (2, 2), oriented counterclockwise.