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malexander

  • 2 years ago

Hi. I wanted to know how does one know when to use the substitution rule for integrals and when not too?

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  1. saifoo.khan
    • 2 years ago
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    @satellite73

  2. lgbasallote
    • 2 years ago
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    take the derivative of u....if that du is present in the integrand you can use sub

  3. satellite73
    • 2 years ago
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    don't use them on saturday night. go out and party

  4. lgbasallote
    • 2 years ago
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    wait...we're talking about u-sub right? not algebraic sub?

  5. lgbasallote
    • 2 years ago
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    lol sat

  6. malexander
    • 2 years ago
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    @lgbasallote yep I am. I wanted to know when you look at an integral problem, how do you know to use either u-substitution or not.

  7. lgbasallote
    • 2 years ago
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    go out and integrate?

  8. lgbasallote
    • 2 years ago
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    @malexander it involves mastery of derivatives...if you know many derivativves you can see them immediately...if not..you can try u-ing then derive it...

  9. satellite73
    • 2 years ago
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    a function multiplied by something that is either the derivative, or a constant multiple of the derivative

  10. satellite73
    • 2 years ago
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    \[\int\sqrt{x^3+3}x^2dx\] for example, because the derivative of \(x^3+3\) is \(3x^2\) and what i wrote above was wrong

  11. satellite73
    • 2 years ago
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    should have been \[\int f(g(x))g'(x)dx\]

  12. lgbasallote
    • 2 years ago
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    ^integral of the chain rule

  13. lgbasallote
    • 2 years ago
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    just noticed lo

  14. lgbasallote
    • 2 years ago
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    lol*

  15. marcoduuuh
    • 2 years ago
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    Don't use it on Sundays either, yolo.

  16. malexander
    • 2 years ago
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    Your confusing me @satellite73. Um. Lets say you have these four integrals (question 2). In this question, which one would you need u-substitution and why?

  17. lgbasallote
    • 2 years ago
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    2c

  18. lgbasallote
    • 2 years ago
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    2b

  19. malexander
    • 2 years ago
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    Why those @lgbasallote ?

  20. lgbasallote
    • 2 years ago
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    \[\large \int \frac{3x^3}{\sqrt{x^4 + 1}} = 3\int \frac{x^3}{\sqrt{x^4 + 1}}\] if i let u = x^4 + 1 du = 4x^3 the constant 4 is not important...but x^3 is...and it is present in the integrand so you can use u-sub

  21. lgbasallote
    • 2 years ago
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    2d is u-subbable too

  22. malexander
    • 2 years ago
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    Oh okay. That makes a bit more sense @lgbasallote . However, I thought we were not able to integrate fractions? (Im a cal 1 student, maybe inter grating fractions is in cal 2)

  23. lgbasallote
    • 2 years ago
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    integrating fractions....for example 1/u^2 1/u^2 = u^(-2) according to basic algebra according to basic integration...you can use power rule on that..i assume you're familiar with that note: NEVER use power rule on 1/u <---the integral of that is automatically ln u

  24. lgbasallote
    • 2 years ago
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    also note that i am using u...this is because u is a function of x meaning it is an expression..not limited to only a variable

  25. malexander
    • 2 years ago
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    right, i remember that @lgbasallote about 1/u^2..and also thats fine, we use "u" in class

  26. malexander
    • 2 years ago
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    @lgbasallote ln is in calc 2, so i hope i get to do that next semester hehe...i think i just need to do more problems with integration then...

  27. lgbasallote
    • 2 years ago
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    i see...so you're just learning u-sub...try integrating the ones i said..2b and 2d

  28. malexander
    • 2 years ago
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    will do!

  29. malexander
    • 2 years ago
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    thanks again @lgbasallote ....i have another question...do u mind me asking it here, or posting another question box?

  30. lgbasallote
    • 2 years ago
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    new post...im too lagged for a long thread lol

  31. malexander
    • 2 years ago
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    LOL! ok sounds good

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