# What is the volume of the solid produced by revolving #f(x)=x^2+3x-sqrtx, x in [0,3] #around the x-axis?

##### 1 Answer

Dec 30, 2016

601.5 cubic units, nearly

#### Explanation:

The two x-scaled and y-scaled graphs reveal that the said

shuttlecock-like solid of revolution has two parts, having just the x-

intercept point

near the origin might appear as a knot. This one has a convex

surface, in contrast to the other that has concave surface.

The volume is

for the limits

between x =. 0 and 3

#=601.5 cubic units, nearly.

graph{0.1(x^2+3x-sqrtx) [-10, 10, -5, 5]}

graph{(10(x^2+3x-sqrtx)) [-0.1, 0.1, -10, 10]}