Mathematics, 18.07.2019 17:10 sanaiajohnson56

If f(x) = -1/x, then f'(x) = 1/x^2. theorem seems to suggest that the integral from -1 to 1 of 1/x^2 dx would equal f(1) - f(-1) = -1 -1 = -2. but 1/x^2 is a positive function and so its integral over [-1,1] should be positive. what is wrong here?

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If f(x) = -1/x, then f'(x) = 1/x^2. theorem seems to suggest that the integral from -1 to 1 of 1/x^2...