Math Problem Statement
Calculate the integral \( \int_0^{2\pi} f(x) \, dx \), where \( f(x) = \begin{cases} \sin(x), & x \leq \pi \\ -6\sin(x), & x > \pi \end{cases} \).
Solution
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Math Problem Analysis
Mathematical Concepts
Integration
Piecewise Functions
Trigonometric Functions
Formulas
Definite Integral Formula \( \int_a^b f(x) \, dx \)
Integration of \( \sin(x) \): \( \int \sin(x) \, dx = -\cos(x) + C \)
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 11-12 or College
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