We sketch the upper and lower bounding curves:

The lower limit of integration is x = 0 (since the question says x ≥ 0).

Next, we need to find where the curves intersect so we know the upper limit of integration.

Equating the 2 expressions and solving:

2x² = x + 1

2x² − x − 1 = 0

(2x + 1)(x − 1) = 0

x = 1 (since we only need to consider x ≥ 0. This is consistent with what we see in the graph above.)

So with y₂ = x + 1 and y₁ = 2x², the volume required is given by:

Here is an indication of the volume we have found. A typical "washer" with outer radius y₂ = x + 1 and inner radius y₁ = 2x² is shown.