Identify the integral to be evaluated.

May 6, 2026Mathematics

ScanSolve AI Answer

May 6, 2026

Answer

8\pi \int_0^{\sqrt{3}} (8-x^2) dx $$

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

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لحساب الحجم، سنقوم بتقييم التكامل الذي تم حسابه في عمل الطالب.
The student's calculation evaluates the definite integral: V = 8 _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 - (x^3)/(3).
(8-x^2) dx = 8x - (x^3)/(3) + C Step 3: Evaluate the definite integral using the Fundamental Theorem of Calculus.

Asked on May 6, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 6, 2026

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 _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 - (x^3)/(3). (8-x^2) dx = 8x - (x^3)/(3) + C Step 3: Evaluate the definite integral using the Fundamental Theorem of Calculus. Apply