## Ldaniel Group Title 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 one year ago one year ago

1. Ldaniel Group Title

What is the approximate area of the strip with respect to x?

2. TuringTest Group Title

the Riemann sum is often written$\sum_{i=0}^nf(x_i^*)\Delta x;~~~\Delta x=(\frac{b-a}n);~~~x_i^*=a+i\Delta x$

3. Ldaniel Group Title

yeah I know I'm having trouble coming up with a formula for the area of the strip

4. TuringTest Group Title

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.

5. Ldaniel Group Title

(a/b)=(x/?) right? .....whats "?"

6. TuringTest Group Title

I do not know what formula you are using

7. Ldaniel Group Title

trying to use similar triangle

8. Ldaniel Group Title

guess that doesn't work out

9. Ldaniel Group Title

b_1 and B_2 has to be something (a-?) but i dont know how to find it

10. Ldaniel Group Title

how would you approximate area of the strip with respect to x?

11. TuringTest Group Title

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 $$f(x+\Delta x)$$

12. Ldaniel Group Title

$Delta(x) \times(x/2)$

13. TuringTest Group Title

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.