Plus42: Integration in Solver
The Plus42 adds an integral function to the solver engine.
Just a Reminder: Get the Plus42 App
Author: Thomas Okken
App:
Android: $9.99
iOS: $9.99
PC/MacOS/Linux: Free
Donations Accepted
Link: https://thomasokken.com/plus42/
Plus42 ∫ Syntax
∫(EXPR:VAR:LLIM:ULIM[:ACC])
EXPR: expression to be integrated
VAR: variable to be integrated
LLIM: lower limit
ULIM: upper limit
ACC: accuracy factor, an optional argument. If ACC is omitted, then Plus42 uses the highest accuracy factor.
Let's take a look at some of the integrals that can be used. In this blog, all results are rounded to four decimal places (FIX 4 is the default setting of Plus42)
Example 1: Basic Integral
I = ∫(x^2 + 1 dx, x = 0, 3)
Solver syntax:
I=∫(X^2+1:X:1:6)
This integral calculates the numerical integral of x^2 + 1 from x = 1 to x = 6. In calculation mode, pressing ( I ) twice would definitely get the result.
Result: I=76.6667
Example 2: Variable Upper Limit
I = ∫(x^3/3 - 2 dx, x = 0, A), A is the upper limit
Solver syntax:
I=∫(X^3÷3-2:X:0:A)
Upper limit known, find the integral:
A = 4; result: I = 13.3333
Integral known, find the upper limit:
I = 4; result: A = 3.3692 (it may take have time depending on the initial guess)
I like how the solver can find both the value of the integrals and solve for the limits of the integral.
Example 3: Variable in the Integrand
I = ∫((x^2 * (x - B)) / (B^2 + x^2) dx, x = 0, 1), B is a variable constant
Solver syntax:
I=∫((X^2×(X-B))÷(B^2+X^2):X:0:1)
B = 1; I = -0.0612
B = 3; I = -0.0784 (I set the initial guess of I = 0)
B can be solved for if you have a good guess and you are willing to wait for the solver to work.
I = -0.07; B = 3.6139
Full Precision: 3.613900797617638382718999085866498
Eddie
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