# how the Calculator finds definite Integrals?

• Sep 7th 2009, 06:53 AM
suboba
how the Calculator finds definite Integrals?
Does anybody know how the ti-83/84 finds definite integrals graphically? For example, you graph a function and want to know the area underneath it between some interval. you go to 2nd>calc>7(def.int.), and put in the upper and lower limits (ti-83/84). It thinks for a second, then shades the area under the curve. How does it do that? I'm not really too concerned w/ how the calculation goes to derive the numerical answer (ie. I assume it calculates the antidervative and uses fundamental theorem) but what i really want to know is how does it know what regeion of the graph to shade.

the concept of the definite integral comes from calculating Riemmen sums (rectangles), but how does the calculator calculate infinite subdivisions?

thanks.
• Sep 7th 2009, 06:59 AM
artvandalay11
from what I know, the calculator uses an approach close to calculating an approximate riemann sum with like 500 rectangles, but the calculator actually uses parabolas, which allow it to trace out curves better for approximation

in terms of simply shading the graph, all it is really doing is connecting points between the function and the x axis, so once it has the function point (x,f(x)) is just draws a line to the point (x,0)