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Ldaniel
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/8-1-2alt.gif
What is the approximate area of the strip with respect to x?
the Riemann sum is often written\[\sum_{i=0}^nf(x_i^*)\Delta x;~~~\Delta x=(\frac{b-a}n);~~~x_i^*=a+i\Delta x\]
yeah I know I'm having trouble coming up with a formula for the area of the strip
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.
(a/b)=(x/?) right? .....whats "?"
I do not know what formula you are using
trying to use similar triangle
guess that doesn't work out
b_1 and B_2 has to be something (a-?) but i dont know how to find it
how would you approximate area of the strip with respect to x?
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 \(f(x+\Delta x)\)
\[Delta(x) \times(x/2)\]
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.