Quick, integrate 2x + sin(y)! Well, frankly, it’s been so long since I’ve done
calculus by hand I can’t remember anymore. Well, knowing calculus is good, but
knowing calc is even more useful!
M-x calc m r (switch to radians mode, which helps with keeping things simple) '2x + sin(y) (The single quote enters algebraic mode) a i y (Calculate the integral with respect to y) Result 1: 2 x y - cos(y)
You can also integrate over specific regions by using C-u a i, whereupon it will
prompt you for the start and end point of the integration.
As the manual mentions, the results are often not as simplified as they could be. Calc is impressive, but it isn’t as sophisticated as Mathematica.
If we take the derivative of the integral we just calculated. We should get back to our original formula.
a d y (Calculate the derivative with respect to y) Result: 1: 2 x + sin(y)
Oh yeah! The system works, people! We can also make the Taylor series of a function:
a t y 6 (Calculate the Taylor series of a term, over y, for 6 terms) Result: 1: 2 x + y - y^3 / 6 + y^5 / 120
We asked for 6 terms, but as the manual mentions, some terms may have coefficient 0, so don’t appear here.
As I mentioned, for simple things this works well, but Calc’s power is limited. However, the integration is customizable - you can write your own integration rules when Calc is missing something. I haven’t been able to find evidence that anyone actually has done this in any add-on package, though. You, reader, can be the first!