Choose a method to find the VOLUME of the solid obtained by rotating the region bounded by he given curves around the indicated line. Include both a 2-D and 3-D picture. State the definite ntegral. Show all work in exact form. xy = 1, y = 0,x = 1,x = 2; about x = -1

Find the exact volume of the solid that results when the rectangular region with vertices at 0, 0, 6, 0, 6, 4 and 0, 4 is revolved about the a x-axis b y-axis

Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the lines x = 9 and y = 5 is revolved about the a) x-axis b) y-axis

Consider the solid whose base is the region bounded by the x-axis, y = x, and y=-4x + 5. Find the volume of the solid if the slices perpendicular to the y-axis are rectangles with height sin(y). Give the exact volume below in the form A + B sin(C) where A, B and C are constants to be determined. Click on the symbol for the equation editor to enter in math mode. b a sin (a) ∞ a

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x² - 15x + 56, y = 0; about the x-axis. Volume =

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = x, y = V about the x-axis Step 1 Rotating a vertical strip between y = x* and y = Vx around the x-axis creates a washerv washer Sketch the region. y 1.5 1.5 1.5 1.5 1.0 1.0 1.0 1.0 0.5 5 0.5 0.5 0.5 -0.5 0.5 1.0 1.5 -0.5 0.5 1.0 1.5 -0.5 0.5 1.0 1.5 -0.5 0.5 1.0 1.5 -0.5 -0.5 -0.5 -0.5 Sketch the solid, and a typical disk or washer. Graph Graph Description Graph Graph Description Graph Graph Description Graph Graph Description 2 2 -2 -1 -2 -2 -1 -2 -1 -2 Step 2 The inner radius of the washer is r and the outer radius is r, =

Find the volume of the solid generated by revolving the region created by the curves, y4 X = 2 and x = 2 about the x-axis. 2 4