## Ldaniel 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/8-1-2alt.gif

1. Ldaniel

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

2. TuringTest

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

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

4. TuringTest

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

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

6. TuringTest

I do not know what formula you are using

7. Ldaniel

trying to use similar triangle

8. Ldaniel

guess that doesn't work out

9. Ldaniel

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

10. Ldaniel

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

11. TuringTest

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

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

13. TuringTest

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.