MethodDisk, washer, and shell are not interchangeable here; this region calls for the disk.
Disk method
V = \pi\int_a^b \big[R(x)\big]^2\,dx
V = \pi\int_{0}^{4}\left(\sqrt{x}\,\right)^{2}dx = \pi\int_{0}^{4} x\,dx
Exact volume of the full region
V = 8\pi \approx 25.1327
lower bound a
0.00
upper bound b
4.00
volume (exact)
25.1327
At the setup's own bounds the numeric integral 25.1327 matches the exact closed form shown above.
Rotating about the x-axis, a slice taken perpendicular to the axis meets the single curve y = sqrt(x) and sweeps a full disk of radius sqrt(x). One curve and no gap, so the disk method fits: the area of each face is pi times the radius squared.
Disk method. Bounds a = 0.00, b = 4.00. Volume 25.1327.
Solid of Revolution Builder: Disk, Washer, and Shell from CalcLearn, free AP Calculus study tools.