Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

I do not know what formula you are using

Answer 7

trying to use similar triangle

Answer 8

guess that doesn't work out

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

\[Delta(x) \times(x/2)\]

Answer 13

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.