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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
 one year ago
 one year 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
 one year ago
 one year ago

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LdanielBest ResponseYou've already chosen the best response.0
What is the approximate area of the strip with respect to x?
 one year ago

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

LdanielBest ResponseYou've already chosen the best response.0
yeah I know I'm having trouble coming up with a formula for the area of the strip
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
the 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.
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
(a/b)=(x/?) right? .....whats "?"
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
I do not know what formula you are using
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
trying to use similar triangle
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
guess that doesn't work out
 one year ago

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

LdanielBest ResponseYou've already chosen the best response.0
how would you approximate area of the strip with respect to x?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
the 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 \(f(x+\Delta x)\)
 one year ago

LdanielBest ResponseYou've already chosen the best response.0
\[Delta(x) \times(x/2)\]
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
it 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.
 one year ago
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