19.4.2  Computing the area under a curve

The area command approximates the area under a graph.

• area takes four arguments:
  • expr, an expression f(x).
  • var=a..b, the variable with a range.
  • n, a positive integer.
  • method, the approximation method to use, which can be one of:
    • trapezoid
    • left_rectangle
    • right_rectangle
    • middle_point
    • simpson
    • rombergt (Romberg with the trapezoid method)
    • rombergm (Romberg with the midpoint method)
    • gauss15 (The 15 point Gaussian quadrature)
• area(expr,var=a..b,n,method) returns an approximation to the area under the graph over the given interval, using the specified method with n subdivisions (or 2ⁿ subdivisions for rombergt, rombergm and gauss15).

Examples