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Answer:

$\displaystyle V = \frac{625 \pi}{2}$

General Formulas and Concepts:

Algebra I

Calculus

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Shell Method: $\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx$

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

Substitute in variables [Shell Method]: $\displaystyle V = 2\pi \int\limits^5_0 {x(x^2)} \, dx$
[Integrand] Multiply: $\displaystyle V = 2\pi \int\limits^5_0 {x^3} \, dx$
[Integral] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^5_0$
Evaluate [Integration Rule - FTC 1]: $\displaystyle V = 2\pi \bigg( \frac{625}{4} \bigg)$
Multiply: $\displaystyle V = \frac{625 \pi}{2}$