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Module 1: Antiderivatives and their graphs

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Graphs of Antiderivatives

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XSIQ
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Advanced Mathematics - Graphs of antiderivatives

Graphs of antiderivatives

Since f(x) is the gradient of F(x) there will be a family of graphs
possible for F(x), the only difference between them being a constant. For
example, if f(x) = 2 we know that F(x) has a constant gradient of 2. So
F(x) could be 2x or 2x + 3 or 2x - 7. F(x) = 2x + c, where c could be any
constant.

To determine the graph of F(x) you will need a point on the graph F(a) = b
or some other information to obtain a unique value for this constant.

The graphs of f(x) and it's antiderivative F(x) are shown on the left.

Where f(x) is a straight line graph with intercept at x = a and F(b) = c
given.

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