Math Problem Statement

Find the length of the curve correct to four decimal places. (Use a calculator or computer to approximate the integral.) r(t) =

t2, t3, t4

, 0 ≤ t ≤ 5

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Calculus
Arc Length
Integration

Formulas

Arc length formula for vector functions: L = ∫ |r'(t)| dt
Derivative of the vector function r'(t) = [2t, 3t^2, 4t^3]
Magnitude of the derivative: |r'(t)| = sqrt((2t)^2 + (3t^2)^2 + (4t^3)^2)

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

College level (Calculus II or III)

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