NIntegral Command

NIntegral( <Function>, <Start x-Value>, <End x-Value> ): Computes (numerically) the definite integral \(\int_a^bf(x)\mathrm\{d}x\) of the given function f, from a (Start x-Value) to b (End x-Value).

NIntegral(ℯ^(-x^2), 0, 1) yields 0.75.

NIntegral( <Function>, <Start x-Value>, <Start y-Value>, <End x-Value> ): Computes (numerically) the indefinite integral of the given function, and plots the graph of that function through (Start x-Value, Start y-Value), with end point at (End x-Value).

NIntegral(sin(x)/x, π, 1, 2π) plots the graph of the indefinite integral \(y=F(x)+c\) of the given function in the interval [π, 2π]. The value of \(c\) is defined by the initial condition (start x-Value, start y-Value)=(π, 1).

Hint: In the CAS View the following syntax can also be used:

NIntegral( <Function>, <Variable>, <Start Value>, <End Value> ): Computes (numerically) the definite integral \(\int_a^bf(t)\mathrm\{d}x\) of the given function f, from a (Start value) to b (End value), with respect to the given variable.

NIntegral(ℯ^(-a^2), a, 0, 1) yields 0.75.