Math Problem Statement
Evaluate the definite integral \( \int_{0}^{\pi} 2 \sin(x) \, dx \).
Solution
To evaluate the definite integral , follow these steps:
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Find the antiderivative: The antiderivative of is .
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Evaluate the definite integral using the limits:
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Calculate the values:
Substituting these values in:
So, the value of the definite integral is .
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Math Problem Analysis
Mathematical Concepts
Definite Integrals
Trigonometric Functions
Formulas
The antiderivative of \( \sin(x) \) is \( -\cos(x) \)
Theorems
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 11-12
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