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Recent content by Tesla3

  1. T

    Arc Length of a curve in polar form

    Hi, Could anybody help me with grasping the arc length concept regarding the polar curve? I have attached the way my book is presenting the concept. So far, I have understood that the angle R is tending to 90 degrees, and that RP tends to r times delta theta, as delta theta tends to zero...
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    Integration involving Hyperbolic Functions Problem

    I did it this way but then realized that I have substituted the wrong limit. Then after rectifying it, I reached the desired conclusion. I have attached my steps.... Thanks for your help PlanetMaster
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    Integration involving Hyperbolic Functions Problem

    Hi, could anybody help me with the following question? I can not figure it out how to find the same constant of proportionality for the rectangular hyperbola. I have attached the book's question and solution as well as my working....... I would be really grateful if anyone can help.
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    Integration involving Inverse Hyperbolic Functions

    Step 11: Step 12: Step 13: Step 14: Step 15: Step 16: Step 17: Step 18: Step 19: Step 20:
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    Integration involving Inverse Hyperbolic Functions

    Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: Step 9: Step 10:
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    Integration involving Inverse Hyperbolic Functions

    I tried to do it using the substitution u=x/2. It gets the required answer but through a trig substitution again which we don't want to use. Although, if I apply integration by parts it is working and leads to the desired result without substitution. I have attached my steps below. PlanetMaster
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    Integration involving Inverse Hyperbolic Functions

    Step 6: Again using integration by parts: Step 7: Step 8: Now we get back the integral in step 3, I am a bit confused, any clue about what went wrong?..... PlanetMaster
  8. T

    Integration involving Inverse Hyperbolic Functions

    Here are my steps....... Integration By Parts Formula I am using: Step 1: Step 2: Step 3: Again we will apply integration by parts....... Then Step 4: Step 5: Should I continue further?........ PlanetMaster
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    Integration involving Inverse Hyperbolic Functions

    Thing is, I tried doing it through integration by parts but it does not work. It only works if I use the substitution. Could you please share the steps if it can be done by integration by parts without substitution. I would be really grateful. PlanetMaster
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    Maclaurin Series Problem

    Could you help me with that other question as well? PlanetMaster I have attached the link to the other question: https://xtremepape.rs/threads/integration-involving-inverse-hyperbolic-functions.52324/
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    Integration involving Inverse Hyperbolic Functions

    Hi, could anybody help me with this integration question? Thing is, I understand the integration process through substitution x = 2sin(u) but there is a notice box in my book suggesting that this could be done without using the substitution x = 2sin(u). I have attached the question from my book...
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    Maclaurin Series Problem

    Thanks for help PlanetMaster There is only one thing that I do not understand in your explanation. Thing is, the part where you say that " We know that k=0, so any fraction with a k in either numerator or denominator is going to be equal to 0. ", is a bit confusing because If any fraction has k...
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    Maclaurin Series Problem

    Could anybody help me with this Maclaurin Series question? I would be really grateful for your help. I have attached the question as in image.
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