Let v be the volume of the solid obtained by rotating about the y-axis the region bounded by y=√x and y=x^2. find v either by slicing (the disk/ washer method) or by cylindrical shells.

The volume of the solid is

Step-by-step explanation:

In this case, the washer method seems to be easier and thus, it is the one I will use.

Since the rotation is around the y-axis we need to change de dependency of our variables to have . Thus, our functions with as independent variable are:

For the washer method, we need to find the area function, which is given by:

By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function and the inner one by . Thus, the area function is:

Now we just need to integrate. The integration limits are easy to find by just solving the equation , which has two solutions and . These are then, our integration limits.

i’m here for points.