Question

To find the volume of the solid obtained by rotating the region enclosed by the curves y=46 √(x−6)

​and y=x−6 about the y-axis, we use the cylindrical shells method and rotate a vertical strip around the y-axis creating a cylinder with radius r= and height h= . Therefore the volume can be found from the integral V=2π∫
6dx

Answer 1

To find the volume of the solid obtained by rotating the region enclosed by two curves about the y-axis, you can use the cylindrical shells method. The volume is calculated by integrating the product of the circumference and height of each cylindrical shell.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region enclosed by the curves y=46 √(x−6) and y=x−6 about the y-axis using the cylindrical shells method, you need to set up the integral V=2π∫ 6dx. This integral represents the sum of the volumes of the cylindrical shells that make up the solid. The radius of each cylindrical shell is the distance from the y-axis to the curve, and the height is the width of the shell.