Math Problem Statement
3integralsqrt(x^2-1)
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometric Substitution
Integration Techniques
Definite and Indefinite Integrals
Formulas
Trigonometric substitution: x = sec(θ), dx = sec(θ) tan(θ) dθ
Reduction formula for secant integrals: ∫ sec^3(θ) dθ = (1/2) sec(θ) tan(θ) + (1/2) ln|sec(θ) + tan(θ)|
Substitution back: θ = sec^(-1)(x)
Theorems
Fundamental Theorem of Calculus
Trigonometric Identities
Suitable Grade Level
University Level (Calculus II or III)
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