anonymous
  • anonymous
Let G(x) be the function defined by G(x) ∶= Area under the curve f(t) = t^-1, between t = 1 and t = x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
i. Express G(x) as a definite integral.
anonymous
  • anonymous
and on [0.6, 1.8]
anonymous
  • anonymous
|dw:1370995838245:dw|

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anonymous
  • anonymous
thank you What is the value of G at x = 1. In other words, what is G(1)?
anonymous
  • anonymous
Integrate the function and plug in 1 for X.
anonymous
  • anonymous
how do you integrate that function without using logs?
anonymous
  • anonymous
..use logs
anonymous
  • anonymous
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anonymous
  • anonymous
\[\int\limits_{}\frac{ 1 }{ t }=\ln|t|\]\[\int\limits_{}\frac{ 1 }{ t }=\ln|t|=\ln|1|=0\]
anonymous
  • anonymous
if we cant use logs then can you attempt it with riemann sums? and if so could someone help me set it up because i did the Rn and Ln and Mn but now i am confused how to proceed
Jhannybean
  • Jhannybean
\[\large \frac{d}{dx} \ln(x) = \frac{1}{x} \ \therefore \ \int\limits \frac{1}{x}dx = \ln(x)\]
anonymous
  • anonymous
You are measuring area either to the left of x=1 or to the right of x=1. When x=1, you are taking the area of a line, which is obviously ZERO! :)
Jhannybean
  • Jhannybean
It would be easier to integrate according to what @FutureMathProfessor stated.... do you HAVE to use reimann's sums in order to find the area? :\
anonymous
  • anonymous
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Jhannybean
  • Jhannybean
Oh you need to find the antiderivative... ah
Jhannybean
  • Jhannybean
That means you havent learned integration yet :(
anonymous
  • anonymous
i have attached the problem above there is q8 and q8 prt 2 and it says if logs are used at all we get no marks
Jhannybean
  • Jhannybean
Yeahh i believe you have to use reimann's sums to figure out the area.
anonymous
  • anonymous
Riemann sums suck!
Jhannybean
  • Jhannybean
Yeeep.
Jhannybean
  • Jhannybean
Do you know how to solve this equation using reimann's sums?
anonymous
  • anonymous
can you do that using just right/left/mid end points or do you have to compute using limits as well? trying to do it thru limits is where i tripped up
Jhannybean
  • Jhannybean
midpoints would be the easiest tbh.
Jhannybean
  • Jhannybean
here is a video that would help you understand how to solve these easier. http://www.youtube.com/watch?v=Jbn81x30uRs
anonymous
  • anonymous
thank you so far video is great! just working thru it now
Jhannybean
  • Jhannybean
awesome

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