Does Definite Integral Always Yield the Area Under the Function
{"Image DocumentName": "Does Definite Integral Always Yield the Area Under the Function?", "Image ImageDescription": "Example: Evaluate the integral . So the area under the function y = sin (2x) from 0 to \uf070 is __? Yes! In a way, it is... Let\u2019s look at the graph: Example: Find the area of the region bounded by the function y = sin (2x) and the x-axis from 0 to \uf070. Solution: If the area of any 2-dimensional region must be positive, simply using the definite integral will not give us the area of the region. Since the answer to the definite integral is 0 and we know the area can\u2019t be 0! What should we do then? We still going to use definite integral to find its area, but we are not going to find it use one definite integral, instead we are going to use two of them (hint: divide the region into two subregions).", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}