Suppose that F (x) = f (x) and F (0) = 3, F (2) = 7. (a) What is the area under y = f

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QUESTION:

Suppose that F (x) = f (x) and F (0) = 3, F (2) = 7. (a) What is the area under y = f (x) over [0, 2] if f (x) 0? (b) What is the graphical interpretation of F (2) F (0) if f (x) takes on both positive and negative values?

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QUESTION:

Suppose that F (x) = f (x) and F (0) = 3, F (2) = 7. (a) What is the area under y = f (x) over [0, 2] if f (x) 0? (b) What is the graphical interpretation of F (2) F (0) if f (x) takes on both positive and negative values?

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Recall that the Fundamental theorem of Calculus states that

         

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