Integral
The definite integral is the area bounded by the graph of a function f(x) between two points a and b. Conventionally, areas above the x-axis (blue) are positive while areas below (yellow) are negative (see Figure).
b
∫ f ′(x) dx = f(b) - f(a)
a
where f ′(x) is the derivative of the function f(x). Some examples are:
| f ′(x) | f(x) | |
|---|---|---|
| c | c x | |
| xc (c ≠ -1) | (c+1)-1 xc+1 | |
| x-1 | ln(|x|) | |
| ec x | c-1 ec x | |
| sin(c x) | -c-1 cos(c x) | |
| cos(c x) | c-1 sin(c x) |
Related units
Last modified:31 December 2025 5.01 p.m.
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