Applications of the definite integral in Geometry, Science and Engineerinf

  1-4 Find the area of the surface generated by revolving the given curve about the -axis. 1.     differentiating w.r.t     Formula for the area of the Surface of revolution ( about -axis):     Substituting (1) and (2) into (3) and integrating over the interval     2.      differentiating … Read more

  1-4 use cylindrical shells to find the volume of the solid generated when the shaded region is revolved about the indicated axis. (1)         (2)     solving and simultaneously             (3)         (4)     Solving             … Read more

  Find the volume of the solid that results when the shaded region is revolved about the indicated axis. (1)     (2)         (3)     Solving for         (4)     Solving for         when , then :         (5)   … Read more

  1-4. Find the area of the shaded region. (1)  The curve lies above the curve and the shaded region is bounded from left side at and from the right side by the line .     (2)   The curve lies above the curve . The two curves intersects at ( the shaded region bounded … Read more