Identify the integral to be evaluated.

لحساب الحجم، سنقوم بتقييم التكامل الذي تم حسابه في عمل الطالب.

Step 1: Identify the integral to be evaluated. The student's calculation evaluates the definite integral: $V = 8\pi \int_0^{\sqrt{3}} (8-x^2) dx$

Step 2: Find the antiderivative of the integrand. The antiderivative of $8-x^2$ with respect to $x$ is $8x - \frac{x^3}{3}$. $\int (8-x^2) dx = 8x - \frac{x^3}{3} + C$

Step 3: Evaluate the definite integral using the Fundamental Theorem of Calculus. Apply