Question

The region between the curve ( y=frac{x}{sqrt{+1}} ) and the ( x )-axis on ( [0,3] ) is rotated about the ( y )-axis. used the shells' method to find the volume of the generated soli

Answer 1

To find the volume of the generated solid using the shells method, divide the region between the curve y = x/sqrt(x+1) and the x-axis on [0,3] into shells. The volume of each shell is 2*pi*x*(x/sqrt(x+1))*dx. Integrate this expression from x=0 to x=3 to find the total volume.

Step-by-step explanation:

To find the volume of the generated solid using the shells method, we first need to find the height of each shell. The height is given by the function y = x/sqrt(x+1). We divide the interval [0,3] into infinitely many shells of thickness dx and radius x. The volume of each shell is given by 2*pi*x*(x/sqrt(x+1))*dx. Integrate this expression from x=0 to x=3 to find the total volume of the solid.