Question

the region bounded by the curves y=x² and y=5 then set up the integral needed to find the volume of the solid generated by revolving this region about the x-axis using the shell method .

Answer 1

To find the volume of the solid generated by revolving the region bounded by the curves y=x² and y=5 about the x-axis using the shell method, we need to set up the integral.

Step-by-step explanation:

To find the volume of the solid generated by revolving the region bounded by the curves y=x² and y=5 about the x-axis using the shell method, we need to set up the integral. The shell method involves integrating the product of the height of the shell and the circumference of the shell. In this case, the height of the shell is the difference between y=5 and y=x², and the circumference of the shell is 2πx. Therefore, the integral for the volume is:

V = ∫[a,b] 2πx (5-x²) dx