Definite Integration How to evaluate. Consider the area

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3_definite_integration.ppt

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>Definite Integration How to evaluate Definite Integration How to evaluate

>Consider the area under a curve Consider the following shaded area: We know that Consider the area under a curve Consider the following shaded area: We know that the area under a curve = If we evaluate the result of the integration using x=a then this is written as:

>Consider the area under a curve Similarly evaluating the result of the integration using Consider the area under a curve Similarly evaluating the result of the integration using x=b gives: The area between x=a and x=b is found by subtracting the area at a from the area at b:

>Consider the area under a curve So, Also, the constant of integration is the Consider the area under a curve So, Also, the constant of integration is the same for both integrals since the same function is used in each integration Hence,

>Example Evaluate Solution: Example Evaluate Solution: