Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Show that if f is Riemann integrable on [a,b] and f(x) ≥ 0 for all x ∈ [a,b],
then

 

The image shows a mathematical expression involving an integral: \[ \int_{a}^{b} f(x) \, dx \geq 0. \] Explanation: - **Integral Symbol (\(\int\))**: Represents the operation of integration. - **Limits of Integration (\(a\) and \(b\))**: These are the boundaries over which the function \(f(x)\) is integrated. - **Function (\(f(x)\))**: The function being integrated with respect to \(x\). - **\(dx\)**: Indicates the variable of integration is \(x\). - **Inequality (\(\geq 0\))**: Specifies that the integral of the function \(f(x)\) over the interval from \(a\) to \(b\) is greater than or equal to zero. This expression suggests that the net area under the curve of \(f(x)\) from \(x = a\) to \(x = b\) is non-negative.
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Transcribed Image Text:The image shows a mathematical expression involving an integral: \[ \int_{a}^{b} f(x) \, dx \geq 0. \] Explanation: - **Integral Symbol (\(\int\))**: Represents the operation of integration. - **Limits of Integration (\(a\) and \(b\))**: These are the boundaries over which the function \(f(x)\) is integrated. - **Function (\(f(x)\))**: The function being integrated with respect to \(x\). - **\(dx\)**: Indicates the variable of integration is \(x\). - **Inequality (\(\geq 0\))**: Specifies that the integral of the function \(f(x)\) over the interval from \(a\) to \(b\) is greater than or equal to zero. This expression suggests that the net area under the curve of \(f(x)\) from \(x = a\) to \(x = b\) is non-negative.
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