

show works please Q6 10 Points The region R is bounded by y = x3, x...
show works please
Q9 10 Points Let R be the region bounded by the curve y = x2 + 1 and the lines x = 0, x = 1, and y = 1. (a) Set up, but do not evaluate, the volume of the solid obtained by rotating R about the x-axis. Show your work. (b) Set up, but do not evaluate, the volume of the solid obtained by rotating R about the line 2 1. Show your work. =
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1Find the area of the region bounded by the curves y 2x2 - 8x + 12 and y=-2 + 12. Find the volume when the area in question/qis revolved around the 3-axis. Find the volume when the area in question/grevolved around the y-axis. Va is revolved around the Ib Find the volume of the region formed when the area enclosed by y = x3 and y 2-axis. Consider only positive values of x. Find the volume...
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(5 pts) Find the area of the region bounded by the graphs of y + 2 and y = [ +1,0 < x < 2. 2 Sketch the region.
Problem 4.(10 points.) Let a region R bounded by x – 3y = 0, x – 3y = 1, y = 0 and y=1. (a) (2 points) Sketch the region R. (b) (8 points) Compute Vy(x – 3y)dxdy
1.The region R is the region bounded by the functions y=x-3 and x=1+y^2. find the volume of the solid obtained by rotating the region R about the y axis. Please include a graph. 2.Find the volume of the solid obtained by rotating the region bounded by the graphs of y=x and y=sqrt(x) about the line x=2. Please include a graph
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Q6 By sketching the graphs, find the area of the region bounded by, y = x4 - 3x2 – 7 and y = x2 + 5. 07 Using integration, find the area of the triangle joining the points whose coordinates are (4,0), (8,6)and (0,4).
1. Sketch the region bounded by the graph of y = – and the x-axis over the interval [1, 3) and then find the area of the region. (10 points)
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
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18) 8. The region is bounded by y = 2 - r- and y = r. (a) (2 marks) Sketch the region. (b) (6 marks) Find the area of the region. (c) (5 marks) Use the method of cylindrical shells to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line r = -3. (d) (5 marks) Use the disk or washer method to...
(10 points) Let R be the region in the first quadrant bounded by the x and y axes and the line y = 1 – 1. Notice R is a triangle with area 1/2 (you do not need to verify this). Find the coordinate of the centroid of R. For extra credit, determine the y coordinate without calculating an integral. (Note: If we regard R as a plate, then the centroid of R can also be thought of as the...