Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 + x² - y² = {(x, y): x² + y² ≤ 9} R = (17√17 - 1) 6 X

1.) Find the area bounded by the regions given by the graphs of y 3x2-10x and y x2+2x. Make sure you know how to find the intersection of the two graphs using algebra. (ans: 24) 2.) Find the area of the region in the first quadrant bounded by the lines y 8x, x 1,y and the curve y (ans: 5/a) .) Use the disk or washer method to setup a definite integral (do not integrate) for the region bounded by the following functions: ys 5-х, y-0 , y-4 ,X-0 about the y-axis. Show the representative rectangle within the region at hand. (ans: Use the same region as in problem#3. Revolve the region about the line y-4. Use Shell method to setup the integral (do not evaluate). Make sure to include the enresentative rectangle within the region at hand. (ans: )

Find the surface area of the portion of the cylinder ya + 2² =9 above tne rectangle in the xy plane. where OEXL2 and -35 ys 3 ........ .. ..... . ....

Find the surface area of the portion of 4x + 3y + 5z = 8 that lies inside the cylinder x² + y² = 49.