Question

Consider the region r in the first quadrant bounded by the x-axis and the line ____. Find the volume of the solid generated by rotating r about the line ____.

Answer 1

To find the volume of the solid generated by rotating a region in the first quadrant bounded by the x-axis and a line about another line, we can use the method of cylindrical shells.

Step-by-step explanation:

To find the volume of the solid generated by rotating a region in the first quadrant bounded by the x-axis and a line about another line, we can use the method of cylindrical shells. We will integrate the area of each shell from 0 to the height of the region.The height of the region can be found by solving the equation of the line for x when y=0. Then, the volume of each shell is equal to the circumference of the shell times the height of the region. Finally, we integrate the volume of each shell from 0 to the height of the region to find the total volume.