AmTran_Bus
  • AmTran_Bus
Integration help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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AmTran_Bus
  • AmTran_Bus
|dw:1440354731938:dw|
AmTran_Bus
  • AmTran_Bus
The integral of x is just (x^2)/2, right?
freckles
  • freckles
yea

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freckles
  • freckles
well +c but we don't care about +c really with definite integrals
AmTran_Bus
  • AmTran_Bus
So I have|dw:1440354893717:dw|
AmTran_Bus
  • AmTran_Bus
or b^2/2 - a^2/2 (1/b-a)?
ganeshie8
  • ganeshie8
right, but nobody leaves it like that.. it can be simplified...
AmTran_Bus
  • AmTran_Bus
|dw:1440355025079:dw| can you help with the bottom?
freckles
  • freckles
\[\frac{1}{2} \frac{b^2-a^2}{b-a}\] hint difference of squares
AmTran_Bus
  • AmTran_Bus
Oh ok. Not too bad then. Can more be done? The book says b+a / 2
freckles
  • freckles
(b+a)/2 is correct
freckles
  • freckles
and you can't do anything else unless you want to write it as b/2+a/2
AmTran_Bus
  • AmTran_Bus
can you show me how you get from 1/2 (b^2-a^2 / 2(b-a) to that?
freckles
  • freckles
do you know the difference of squares formula...
freckles
  • freckles
that was my hint
freckles
  • freckles
so maybe not.. b^2-a^2=(b-a)(b+a)
AmTran_Bus
  • AmTran_Bus
Ok thanks that was the missing piece for me I guess.
freckles
  • freckles
hmmm how did you get that extra 2 ?
freckles
  • freckles
\[\frac{1}{b-a} \int\limits_a^b x dx \\ \frac{1}{b-a} \cdot \frac{x^2}{2}|_a^b \\ \frac{1}{b-a}(\frac{b^2}{2}-\frac{a^2}{2} ) \\ \frac{1}{b-a} (\frac{b^2-a^2}{2}) \\ \frac{1}{2} \frac{b^2-a^2}{b-a} \\ \frac{1}{2} \frac{(b-a)(b+a)}{b-a}\] you should just have one 2 on bottom not two 2's
freckles
  • freckles
"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?
AmTran_Bus
  • AmTran_Bus
Oh me! Yes, I accidentally put in an extra 2 on the bottom, forgetting the 1/2!
freckles
  • freckles
oh okay

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