MAT136H1 Lecture : 5.2 Integration & Anti-derivatives Definite Integrals Question #4 (Medium)
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Question #4 (medium): evaluating integrals in terms of areas. If the graph is not provided with the question, drawing the function helps visualize the geometric shapes to calculate in terms areas. Calculate the area of the geometric shapes that are usually divided by the - intercepts or other grid lines where the curve changes its course. Lastly sum up the areas as the total area under the function given by the definite integral. Evaluate the integral by interpreting in terms of areas. Since the graph is not given, drawing the graph of the absolute value function over the interval will help visualize better to calculate the definite integral in terms of areas. Since the -intercept is at ( ), the integral can be split into the area of two triangles: the first triangle over the interval [ ] has and | ( ) | . Therefore the: the second triangle over the interval [ ]has and.
