Integrals

You can use Desmos to investigate the beautiful world of integral calculus. Simply type int to get started. Then, fill in the lower bound, upper bound, and the integrand and you'll be on your way!

You can find the integral on the Desmos keyboard by clicking on FUNCTIONS and then MISC. Or, as a shortcut, try typing int directly into the expression line.

 

You can graph a definite integral by filling in the upper bound, lower bound, and integrand. Don't forget to include dx if integrating with respect to x.

 

It's also possible to graph the output of some indefinite integrals by including x in the upper bound, 0 in the lower bound, and integrating with respect to a variable other than x.

 
 

 

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6 Comments

  • 0
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    Jennifer Broekman

    I tried to integrate a function defined by an integral, so that I could plot both velocity and position based on a (piecewise) acceleration function, but that didn't work. Is my syntax wrong, or is the repeated integral not possible (yet)?

  • 0
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    Ruban SriramBabu

    Unfortunately there is no integral option in the desmos mobile app for android. Hope you guys can add this feature in the next update of the app. Otherwise great app. Thanks in advance.

  • 1
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    Anonimous_User

    I had the same problem where I couldn't integrate a function whose definition was an integral. I wanted to do a simulation sort of thing with acceleration, velocity, and position.

  • 2
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    T Chip Webb

    @Jennifer Broekman I messed around with your graph. Apparently Desmos doesn't handle an integration using a function that is itself an integration. Namely h(s). It just goes out to lunch. Sometimes it comes back minutes later, apparently having had too much to drink during lunch.

    If you replace the integrated function with j(r) (instead of g(r)) where j(r) is f(x) manually integrated, then your graph works. 

    Edited by T Chip Webb
  • 0
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    Hckellylee

    I understand why you let the upperbound be x (infinity essentially right?), but why do you let the lower bound be 0? 

  • 0
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    Bill Calhoun

    @Jennifer Broekman - It seems that Desmos is perfectly happy to integrate a continuous function twice - see https://www.desmos.com/calculator/v3rjhjaivg.

    I'm actually amazed that Desmos can integrate a piecewise function even once, but if that result is also piecewise, Desmos is unhappy with the second integration. The only workaround I've found, as @T Chip Webb suggested above, is to explicitly redefine the first integral as a new function and then integrate that. See https://www.desmos.com/calculator/myyvey4jq6.

     

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