Final answer:
The volume of the solid obtained by rotating the bounded region about x=10 can be calculated using the cylindrical shells method, by integrating the volume of thin shells from x=1 to x=10.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by the curves x = y², x = 1, and x = 10 about the line x = 10, we can use the method of cylindrical shells. The volume of a thin shell with radius r and height h, revolving around the line x = 10 is given by the formula V = 2πrh².
The radius of the shell is the distance from x to 10, which is 10 - x. The height of the shell is given by the function y, that is y(x) or simply √x. We integrate from x = 1 to x = 10 since these are the bounds described by the region.
Therefore, the integral to compute the volume is V = ∫1102π(10 - x)√x dx. After solving the integral, we would obtain the total volume. However, in this answer, we are not performing the actual calculation but explaining the method to approach the problem.