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Sujay

  • 2 years ago

How do you evaluate the following integral analytically (no graphs, or calculators)?

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  1. Sujay
    • 2 years ago
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    \[\int\limits_{0}^{5}\left| (x^2-5x+4) \right| dx\]

  2. Sujay
    • 2 years ago
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    Thanks! How did you get those 3 parts (this is kinda dumb, but sorry).

  3. sami-21
    • 2 years ago
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    when you put x=1 the absolute value is positive when you put x=2 and three absolute value is negative (thats why i put - sign in front of second integral ) for x=4 and 5 absolute value is again positive .

  4. Sujay
    • 2 years ago
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    Isn't it 0 @ 1?

  5. sami-21
    • 2 years ago
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    yes it is because at x=0 still abs (x^-5x+4) =(0-0+4)=4 positive .

  6. Sujay
    • 2 years ago
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    Should the second integral be from 1 to 4 instead of 1 to 3, and the third integral be from 4 to 5?

  7. sami-21
    • 2 years ago
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    at x=1 yes zero .

  8. Sujay
    • 2 years ago
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    so the second integral should be from 1 to 4, and the 3rd one 4 to 5?

  9. sami-21
    • 2 years ago
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    sorry i wrote it wrong . you are right first from 0..1 second from 1..4 and third from 4..5

  10. sami-21
    • 2 years ago
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    \[\Large \int\limits_{0}^{1} (x^2-5x+4)dx-\int\limits_{1}^{4} (x^2-5x+4)dx+\int\limits_{4}^{5}(x^2-5x+4)dx\]

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