MAT136H1 Lecture : 6.1 Areas Between Curves Question #6 (Medium)
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Question #6 (medium): finding the missing variable from the area between two functions. After establishing the expression for the area bound by two functions [ ( ) ( )] backwards to find any missing variable. Graph the area bound by the functions as a helpful guide which helps to see which function lies at the top and bottom. Setting the right order of [ ( ) ( )] is very important. Then the rest of the calculation is applying various integral properties to simplify and finding the missing variable. Find the value of where the region enclosed by the functions and is . The given functions are written in terms of . Graphing the functions also indicate that the integral. Since sets the right boundary, should be done over . ; and since sets the left boundary, . So equating into the first function: ; and into the second equation: . , so the -intercepts are the same at .
