Definite Integration How to evaluate
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 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 same for both integrals since the same function is used in each integration Hence,
Example Evaluate Solution: