In: Math
Consider the region illustrated below, bounded above by ? = ?(?) = 10 cos ( ?? 9 ) and below by ? = ?(?) = ? −?+3 . The curves intersect at the points (?, ?(?)) and (?, ?(?)), where 0 < ? < ? < 5. Do not try to find or estimate the values of ? or ?.
a. The total area of the region.
b. The volume of the solid that has this region as its base, where cross-sections perpendicular to the ?-axis are semicircles with their diameters on the xy-plane.
c. The volume of the solid that results by revolving this region about the x-axis.
d. The volume of the solid that results by revolving this region about the line ? = 5.