precal
  • precal
Definite Integral - need help with this one
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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precal
  • precal
\[\int\limits_{1}^{5}(1-x) dx\]
precal
  • precal
I have to use the limits of sums
precal
  • precal
@amistre64 can you help me on this one? Thanks

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precal
  • precal
\[\int\limits_{1}^{5}(1-x) dx = \sum_{x=1}^{5}(1-x) \Delta x\]
precal
  • precal
I know my delta x is 4/n but I am not sure how to find x I thought it was \[\frac{4i}{n}\]
amistre64
  • amistre64
your x is the start of your interval + the subdivisions of the rest of it added up
amistre64
  • amistre64
x = 1 + 4i/n
amistre64
  • amistre64
then as n moves towards infinity your inteval is chopped up into infintesimal bits
amistre64
  • amistre64
try this; spose x moves from 2 to 12 how would you write up an equivalent part for x
precal
  • precal
2+6i/n but I am guessing
amistre64
  • amistre64
think of it as \[I=[a,b]\]\[x=a+(b-a)\frac{i}{n}\]
precal
  • precal
|dw:1332884773241:dw|
precal
  • precal
Is this how I am suppose to set it up? I will need to work it out and verify that the final solution comes out to -8.
amistre64
  • amistre64
that looks good to me; except that inf is alittle to upright for my tastes
precal
  • precal
back to your question earlier it is 2 + (10i)/n is that correct?
amistre64
  • amistre64
yes :)
precal
  • precal
|dw:1332884974304:dw|
precal
  • precal
Sorry, I was having a hard time using the equation editor so I decided to draw it. I did not realize I had made an eight. Thanks, I have to go run an errand but this will help me finish some other problems. I struggle to make the connection between definite integrals and the summations plus limits. I know the connection is important but yet I struggle. My math journey continues......... Thanks :)
amistre64
  • amistre64
good luck ;)

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