Set up and solve a double integral to find the area of the surface f(x,y) =...
1. Set up, but do not evaluate, an integral to find the area enclosed by the x-axis and the [x = 1 + et curve ly = t-t2 2. {*5+?2t Osts2 y = VE (1) Find the equation of the tangent line at the point where t = (2) Set up, but do NOT evaluate, an integral to find the area of the surface obtained by rotating the curve about the y-axis. 3. Set up but do NOT evaluate an...
Evaluate the surface integral f(x,y,z) dS using a parametric description of the surface. f(xyz) = 4x, where S is the cylinder X + z2-25, 0 ys2 The value of the surface integral is (Type exact answers, using T as needed.) Find the area of the following surface using the given explicit description of the surface. The cone z2 = (x2 +y2) , for Oszs8 Set up the surface integral for the given function over the given surface S as a...
With double integral find surface area when y=e", y = x, y = 4 and axis y with y <et
a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically. a. Set up an integral for the area of the surface generated by revolving the curve x = 3 sin y, 0 sys about the y-axis. b. Graph the curve. c. Use technology to find the surface area numerically.
Set up the integral to represent the surface area of the solid obtained by revolving y=x^2 + sin(2x) on the interval [ 0, (π/2) ] about the x-axis. DO NOT solve.
Set up an integral to find the volume under the graph of f(x, y) = e xy sin(x) and above the region x ^2 + y ^2 ≤ 64 in the xy-plane
Evaluate the Surface Integral, double integral F*ds, where F = [(e^x)cos(yz), (x^2)y, (z^2)(e^2x)] and S is a part of the cylinder 4y^2 + z^2 =4 that lies above the xy plane and between x=0 and x=2 with upward orientation (oriented in the direction of the positive z-axis). ASAP PLEASE
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane. 4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
1.1. Find the absolute and minimum values of f(x, y) = xy? on the set D= {(x, y)\x² + y si 1.2. Find the extreme values of f(x,y) = x² + y2 + 4x-4y, using the Lagrange multipliers, with the constraint x² + y² 59 1.3. Evaluate the integral - Le*dxdy 1.4. Evaluate the integral L1.** sin(x+ + gydydx 1.5. Find the area of the surface x + y2 +22 - 4 that lies above the plane z = 1....
(a) Set up a double integral for calculating the flux of the vector field F(x, y, z) = (x2, yz, zº) through the open-ended circular cylinder of radius 5 and height 4 with its base on the xy-plane and centered about the positive z-axis, oriented away from the z-axis. If necessary, enter 6 as theta. Flux = -MIT" dz de A= BE C= D= (b) Evaluate the integral. Flux = S]