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Numerical Integral

The TI-30X Pro MathPrint™ calculates the (approximate) numerical integral of an expression with respect to a variable x, given a lower limit, an upper limit and a tolerance for the numerical method.

MathPrint™ Mode

% Q pastes the numerical integral template from the keypad to calculate the numerical integral on a given interval with the default tolerance H is 1EM5.

Example in RADIAN Angle Mode

% Q

q " <

% Q

0 " g " "

z X z ) "

<

To change the default tolerance, H, and observe how the tolerance plays a role in the numerical solution, paste the numerical integral from the menu location, d MATH 8:fnInt(, where the numerical integral template will paste with the option to modify the tolerance as needed for an investigation of the numerical integral result.

Example in DEGREE Angle Mode

d MATH 8:fnInt(

with optional tolerance

q <

d 8

0 " 3 "

z G 5 <

Classic Mode or Entry

In Classic mode or in classic edit lines, the fnInt( command will paste from the keypad or MATH menu.

Syntax: fnInt(expression,variable,upper,lower[,tolerance]) where tolerance is optional and the default H is 1EM5.

Example

% Q

or

d MATH 8:fnInt(

% Q

z G 5 % .

z % .0 % .3 )

<

³ Problem

Find the area under the curve f(x) = Mx2+4 on the x intervals from M2 to 0 and then from 0 to 2. What do you notice about the results? What could you say about the graph of this function?

% Q M 2 " 0 "

M z F T 4 " r

<

# # <

% ! " 0 J

" 2

<

Notice that both areas are equal. Since this is a parabola with the vertex at (0,4) and zeros at (M2,0) and (2,0) you see that the symmetric areas are equal.