A Peculiar Property of Definite Integrals // The King Rule (The Art of Integration)

Comments · 44

• PH

  @philiplee3925 · 3 years ago

  This is underrated

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• MA

  @mattikemppinen6750 · 3 years ago

  Very clear and concise explanation, thanks! Just learned about this property, it's a great addition to anyone's bag of integration tricks =)

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• JO

  @johanndohmann1281 · 2 years ago

  Great Video.Thanks a lot.  Your "trig" identities are "tricky" identities as well.  Best wishes from germany

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• MI

  @mihaipuiu6231 · 2 years ago

  Your writing is very nice and your explanation is the same. I'd prefer all the teachers to be like you. Thanks.

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• RE

  @recipehill · 5 years ago

  numste sir ji

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• TO

  @tomctutor · 1 year ago (edited)

  Alternative method of this proof is by applying the <b>shift formula</b> for definite integrals;<br>∫ f(x)dx , from &apos;a&apos; to &apos;b&apos;= ∫ f(-x)d(-x), from &apos;-a&apos; to &apos;-b&apos; .. <i>this part is simply t-sub with t= -x</i> <br>= - ∫ f(-x)dx, from &apos;-a&apos; to &apos;-b&apos;<br>= - ∫ f(-(x-c))d(x-c), from &apos;-a +c&apos; to &apos;-b +c&apos; &nbsp;.. <i>this part is essentially the shift formula by constant c for the variable</i><br>= - ∫ f(-(x-c))[d(x-c)/dx]dx, from &apos;-a +c&apos; to &apos;-b +c&apos; .. note d(x-c)/dx = 1<br>= - ∫ f(-(x-c) dx, from &apos;-a +c&apos; to &apos;-b +c&apos;<br>Now let constant c= a+b,<br>= - ∫ f(-(x-a-b)) dx, from &apos;-a +a+b&apos; to &apos;-b +a+b&apos;<br>= - ∫ f(-(x-a-b)) dx, from &apos;b&apos; to &apos;a&apos;<br>= - ∫ f(a+b -x) dx, from &apos;b&apos; to &apos;a&apos;<br>= &nbsp;∫ f(a+b -x) dx, from &apos;a&apos; to &apos;b&apos; ∎<br><br>Thankyou for the fine examples.

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• PA

  @pahmancanteat2637 · 1 year ago

  Underrated 🥹🥹🥹🥹🥹

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• SF

  @sfatimabatool8ij72 · 3 months ago

  Thanks I&apos;m in 12th grade rn this really helped me

• NE

  @negativeM · 11 months ago

  Thank you for posting this! I want to see some series videos from you. Your content is just amazing. Nice well balanced teaching style. Keep posting this content please.

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• TW

  @TwilightAndrew · 1 year ago

  THanks very much!! Really helpful!

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• OO

  @oof2713 · 1 year ago

  concise!

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• İR

  @İrmikehe · 1 year ago

  Hi I am from Turkey and I am going to high school we have to learn integral and our teachers dont now this type problems<br>This metod made my job easier thanks a lot

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