Question

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.

Answer 1

Answer:

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}.