Mathematics: Please help, I give brainliest.

Please help, I give brainliest. - id13291225, joel3410

Ответ:

julio003620

10.09.2021

Mathematics

a. $\displaystyle AL = \int\limits^5_2 {\sqrt{1+ \frac{9}{x^2}} \, dx$

b. $\displaystyle AL = 4.10322$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Integration

IntegralsDefinite IntegralsIntegration Constant C

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

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

U-Substitution

Arc Length Formula [Rectangular]: $\displaystyle AL = \int\limits^b_a {\sqrt{1+ [f'(x)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

y = 3ln(x)

Interval [2, 5]

Step 2: Find Arc Length

[Function] Differentiate [Logarithmic Differentiation]: $\displaystyle \frac{dy}{dx} = \frac{3}{x}$ Substitute in variables [Arc Length Formula - Rectangular]: $\displaystyle AL = \int\limits^5_2 {\sqrt{1+ [\frac{3}{x}]^2}} \, dx$ [Integrand] Simplify: $\displaystyle AL = \int\limits^5_2 {\sqrt{1+ \frac{9}{x^2}} \, dx$ [Integral] Evaluate: $\displaystyle AL = 4.10322$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e

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