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?

The flaw is at x=0 where the function is not defined

Step-by-step explanation:

For any function we have

The integral can be evaluated only if the function f(x) is defined in the interval [a,b] in which this integral is evaluated

In our our case function f(x) is not defined at x=0 in the interval [-1,+1] thus this results in the flaw that we have obtained in the reasoning

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.

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