Final answer:
To find the volume of the solid generated by revolving the region enclosed by the given graphs about the x-axis, we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region enclosed by the graphs of y=e^(x/2), y=1, and x=ln(5) about the x-axis, we can use the method of cylindrical shells.
First, let's find the limits of integration. Since y=1 is a horizontal line and y=e^(x/2) is always greater than 1, the region enclosed is above y=1.
To find the volume, we integrate the circumference of each shell (2πr) multiplied by its height (dx) from x=ln(5) to x=0, where x=ln(5) is the point of intersection between the two graphs. The radius of the shell is given by r=y-1.
So, the volume V is given by the integral V = ∫(2π(y-1))dx, where x goes from ln(5) to 0. Evaluating this integral will give us the volume of the solid generated.