A solid lies between planes perpendicular to the x-axis at x = 0 and x = 17. The cross-sections perpendicular to the axis on the interval 0 ≤ x ≤ 17 are squares with diagonals that run from the parabola y = - 2 √x to the parabola y = 2 √x.

Find the volume of the solid.

Therefore, we get that the volume of the solid is V=8/3 · 17^{3/2}.

Step-by-step explanation:

From exercise we have that

0 ≤ x ≤ 17

y = - 2 √x and y = 2 √x.

We calculate the volume of the solid, we get:

/int/limits^17_0 / int/limits^{2 √x}_{-2 √x} {1} /, dy /, dx=

=/int/limits^17_0 [y]/limits^{2 √x}_{-2 √x} /, dx

=/int/limits^17_0 { (2 √x+2 √x) } /, dx

=4/int/limits^17_0 {√x} /, dx

=4 · 2/3 [x]/limits^17_0

=8/3 · 17^{3/2}

Therefore, we get that the volume of the solid is V=8/3 · 17^{3/2}.