The parabolic arc y = √x, 1 ≤ x ≤ 2 is revolved around the x-axis. The volume of the solid of revolution is

Concept:

Revolution about x-axis: The volume of the solid generated by the revolution about the x-axis, of the area bounded by the curve y = f(x), the x-axis and the ordinates x = a and x = b is

\(V = \mathop \smallint \nolimits_a^b π {y^2}dx\)

similarly for revolution about y-axis:

\(V=\int \pi {{x}^{2}}dy\)

Calculation:

Given:

\(V = \mathop \smallint \limits_1^2 \pi{y^2}dx\)

\(V = \frac{{3\pi }}{2}\)

Hence the required volume will be \(\frac{3\pi}{2}\).