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AmTran_Bus

  • one year ago

Integration help

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  1. AmTran_Bus
    • one year ago
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    |dw:1440354731938:dw|

  2. AmTran_Bus
    • one year ago
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    The integral of x is just (x^2)/2, right?

  3. freckles
    • one year ago
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    yea

  4. freckles
    • one year ago
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    well +c but we don't care about +c really with definite integrals

  5. AmTran_Bus
    • one year ago
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    So I have|dw:1440354893717:dw|

  6. AmTran_Bus
    • one year ago
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    or b^2/2 - a^2/2 (1/b-a)?

  7. ganeshie8
    • one year ago
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    right, but nobody leaves it like that.. it can be simplified...

  8. AmTran_Bus
    • one year ago
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    |dw:1440355025079:dw| can you help with the bottom?

  9. freckles
    • one year ago
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    \[\frac{1}{2} \frac{b^2-a^2}{b-a}\] hint difference of squares

  10. AmTran_Bus
    • one year ago
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    Oh ok. Not too bad then. Can more be done? The book says b+a / 2

  11. freckles
    • one year ago
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    (b+a)/2 is correct

  12. freckles
    • one year ago
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    and you can't do anything else unless you want to write it as b/2+a/2

  13. AmTran_Bus
    • one year ago
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    can you show me how you get from 1/2 (b^2-a^2 / 2(b-a) to that?

  14. freckles
    • one year ago
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    do you know the difference of squares formula...

  15. freckles
    • one year ago
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    that was my hint

  16. freckles
    • one year ago
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    so maybe not.. b^2-a^2=(b-a)(b+a)

  17. AmTran_Bus
    • one year ago
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    Ok thanks that was the missing piece for me I guess.

  18. freckles
    • one year ago
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    hmmm how did you get that extra 2 ?

  19. freckles
    • one year ago
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    \[\frac{1}{b-a} \int\limits_a^b x dx \\ \frac{1}{b-a} \cdot \frac{x^2}{2}|_a^b \\ \frac{1}{b-a}(\frac{b^2}{2}-\frac{a^2}{2} ) \\ \frac{1}{b-a} (\frac{b^2-a^2}{2}) \\ \frac{1}{2} \frac{b^2-a^2}{b-a} \\ \frac{1}{2} \frac{(b-a)(b+a)}{b-a}\] you should just have one 2 on bottom not two 2's

  20. freckles
    • one year ago
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    "can you show me how you get from 1/2 (b^2-a^2 / 2(b-a) to that?" or was the extra 2 just a type-o?

  21. AmTran_Bus
    • one year ago
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    Oh me! Yes, I accidentally put in an extra 2 on the bottom, forgetting the 1/2!

  22. freckles
    • one year ago
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    oh okay

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