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Section 4.2 Definite Integral Math 1231: Single-Variable Calculus
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Definite Integral: Definition
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Net Area (Signed Area)
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Existence of Definite Integral Theorem If f is continuous on [a, b], or if f has only a finite number of jump discontinuities, then f is integrable on [a, b]; that is, the definite integral exists.
![Existence of Definite Integral Theorem If f is continuous on [a, b], or if f has only a finite number of jump discontinuities, then f is integrable on [a, b]; that is, the definite integral exists.](http://images.slideplayer.com./26/8638029/slides/slide_6.jpg "Existence of Definite Integral Theorem If f is continuous on [a, b], or if f has only a finite number of jump discontinuities, then f is integrable on [a, b]; that is, the definite integral exists.")
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Evaluate Integrals How to evaluate integrals? 1.Interpret the integrals in terms of areas. 2.Fundamental Theorem of Calculus. 3.Other techniques.
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Examples Example Evaluate the following integral by interpreting it in term of (signed) areas. The integral is equal to the area of blue region, which is a quarter circle of radius 1.
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Properties of the Integral
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Examples Example
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Evan and Odd Functions
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More Examples
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