Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometric substitution
Calculus
Integration techniques
Formulas
Substitution: x = 3 sec(θ)
Pythagorean identity: sec^2(θ) - 1 = tan^2(θ)
Integral of sec^2(θ): ∫ sec^2(θ) dθ = tan(θ)
Derivative of sec(θ): d/dθ [sec(θ)] = sec(θ)tan(θ)
Theorems
Pythagorean trigonometric identities
Fundamental Theorem of Calculus
Suitable Grade Level
Undergraduate Calculus
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