[4] Sketch the region bounded above the curve of y = x2 - 6, below y...
The region R is bounded by the x-axis and y = V16 – x2 a) Sketch the bounded region R. Label your graph. b) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) da c) R
1. Find the mass and centroid of the region bounded by the = y2 with p (a, y) parabolas y x2 and x 2. Set up the iterated (double) integral(s) needed to calculate the surface area of the portion of z 4 2 that is above the region {(«, у) | 2, x < y4} R 2 Perform the first integration in order to reduce the double integral into a single integral. Use a calculator to numerically evaluate the single...
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 - x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Ry region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. sec(x2 + y2) tan(x2 + y2) dA R
2) The region R is bounded by the x-axis and y = V16 – x2 a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
2) The region R is bounded by the x-axis and y = V16 – x2. a) (0.75 point) Sketch the bounded region R. Label your graph. b) (0.75 point) Set up the iterated integral to solve for the area of the bounded region using either the Rx region or Ry region. Do not integrate. c) (1.25 point) Evaluate the integral using polar coordinates for the region R. S sec(x2 + y2) tan(x2 + y2) da R
show all work 1. Find the area of the region bounded by the curves below. Sketch a graph of the region first. a. x = y2, x = VD, y = 0 b. y = x2 – 4, y == x2 + 4
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integration R in Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte-gral which represents the volume of the ice cream cone bounded by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume =∫∫drdθ. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
1. Let E be the solid region bounded above by the sphere 4 = x2 + y2 + z2 and below by the plane y-z =-2. a. Generate a 3D picture of the region E using 3D graphing software. b. Write the integral J [ f(x,y,z)dVas an iterated integral (in rectangular coordinates) in two different ways - one with integration with respect to z first, and one with integration with respect to y first.