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Ldaniel

  • 3 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

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  1. Ldaniel
    • 3 years ago
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    What is the approximate area of the strip with respect to x?

  2. TuringTest
    • 3 years ago
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    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
    • 3 years ago
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    yeah I know I'm having trouble coming up with a formula for the area of the strip

  4. TuringTest
    • 3 years ago
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    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
    • 3 years ago
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    (a/b)=(x/?) right? .....whats "?"

  6. TuringTest
    • 3 years ago
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    I do not know what formula you are using

  7. Ldaniel
    • 3 years ago
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    trying to use similar triangle

  8. Ldaniel
    • 3 years ago
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    guess that doesn't work out

  9. Ldaniel
    • 3 years ago
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    b_1 and B_2 has to be something (a-?) but i dont know how to find it

  10. Ldaniel
    • 3 years ago
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    how would you approximate area of the strip with respect to x?

  11. TuringTest
    • 3 years ago
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    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
    • 3 years ago
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    \[Delta(x) \times(x/2)\]

  13. TuringTest
    • 3 years ago
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    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.

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