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By extending the ideas that lead to the idea of Riemann Sums allows us to interpret a definite integral as the “Area Under the Curve.” If the integrated \(f(x)\) is above the x-axis then the area is positive, whereas, if \(f(x)\) is below the x-axis then the area is negative. 

\(\texttt{Area Under The Curve}=\displaystyle\int_a^b f(x) dx \)

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Practice Problems

Determine the area of the enclosed region. 

Suggestive Solution Guide