# Math Insight

### Applet: Indefinite integral of a function

The function $f(x)$ is plotted by the thick blue curve. If it can be calculated, the function's indefinite integral $\int f(x) dx$ is shown by the thin red curve. You can move the large green diamond along the graph of $\int f(x)dx$ by dragging with your mouse; its $x$-coordinate is $x_0$. A tangent line to $\int f(x)dx$ calculated at $x=x_0$ is shown by the green line. Its slope is the value $f(x_0)$ of the function $f$ itself evaluated at $x=x_0$. This slope is also displayed by the smaller green diamond on the graph of $f$, which is at the point $(x_0,f(x_0))$. As you change $x_0$, this smaller diamond representing the slope traces out the graph of the function itself. You can change $f(x)$ by typing a new value in its box. The value of $\int f(x)(x)$ is displayed to the right of the box. Since you can always add an arbitrary constant $C$ to the integral, you can move the graph of $\int f(x) dx$ up and down by dragging the red point. You can hide items by unchecking the corresponding check boxes in order to test yourself on how well you can determine the indefinite integral from the function or vice versa.

You can use the buttons at the top to zoom in and out as well as pan the view.

Applet file: indefinite_integral_function.ggb