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 2 years ago
Write a Riemann sum and then a definite integral representing the area of the region, using the strip shown in the figure below where a = 6 and b = 12. Evaluate the integral exactly. Use your work to answer the questions below.
http://www.webassign.net/hgmcalc/812alt.gif
 2 years ago
Write a Riemann sum and then a definite integral representing the area of the region, using the strip shown in the figure below where a = 6 and b = 12. Evaluate the integral exactly. Use your work to answer the questions below. http://www.webassign.net/hgmcalc/812alt.gif

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Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0What is the approximate area of the strip with respect to x?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0the Riemann sum is often written\[\sum_{i=0}^nf(x_i^*)\Delta x;~~~\Delta x=(\frac{ba}n);~~~x_i^*=a+i\Delta x\]

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0yeah I know I'm having trouble coming up with a formula for the area of the strip

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0the strip is a trapezoid, so you can use the formula\[A=(\frac{b_1+b_2}2)h\]in this case, the height of the trapezoid is \(\Delta x\) and the bases are the value of the function at two different points.

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0(a/b)=(x/?) right? .....whats "?"

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0I do not know what formula you are using

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0trying to use similar triangle

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0guess that doesn't work out

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0b_1 and B_2 has to be something (a?) but i dont know how to find it

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0how would you approximate area of the strip with respect to x?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0the way your picture is, \(x\) seems to be going from right to left, and \(x+\Delta x\) the left side, so the bases are \(f(x)\) and \(f(x+\Delta x)\)

Ldaniel
 2 years ago
Best ResponseYou've already chosen the best response.0\[Delta(x) \times(x/2)\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.0it will be\[\Delta x[\frac{f(x)+f(x+\Delta x)}2]\]so you need to figure our what f(x) is. Remember that this is a line; you can fine its slope.
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