YOU HAVE TO READ STEPS 1 TO 3 IN ORDER TO DO 4. JUST NEED TO KNOW 4

Use the shell method to find the volume of the solid below the surface of revolution and above the xy-plane. The curve 2 = 25in(y), (O S y S if), in the yzplane is revolved about the z-axis. Step 1 Observe that the region is bounded by the graph of the equation 2 = 25in y (0 S y S n) as shown beiow, and consider a verticaE rectangle in the given region. Then the axis of revolution in the yz-plane is vertical .2 vertical Step 2 b To find the volume in the yz-plane, use the shell method, which states that volume is given by V = 2n] p(y)h(y) dy for a a the distance from the center of the rectangle to the vertical axis of revolution and My) represents the height v' vertical y ,4 height _;.A vertical of the rectangle. axis of revolution, where p(y) is Step 3 Write the height of the rectangle between the surface of the curve and the xy-plane. My) = 2 sin(y) V 28in (y) Substitute the values of p(y), My), a and b into the integral for volume and integrate by parts. V 71' 271/ y(25in y) dy 0 2n[ ]