To approximate the integral $\int_2^4 \sqrt{3x} \, dx$ using a right Riemann sum with 11 rectangles, follow these steps in a spreadsheet:

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Steps for Spreadsheet Computation:

1. Determine the width of each rectangle ($\Delta x$):
   $\Delta x = \frac{b - a}{n} = \frac{4 - 2}{11} = \frac{2}{11} \approx 0.181818$

2. Right-end points:
   The $x$-values are: $x_i = 2 + i \cdot \Delta x \quad \text{for } i = 1, 2, \ldots, 11$

3. Function values at right-end points:
   Compute $f(x_i) = \sqrt{3x_i}$.

4. Sum the areas of the rectangles:
   Multiply each function value by $\Delta x$ and sum them.

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Example of Spreadsheet Setup:

• Column A: Row numbers $i$ (1 to 11).
• Column B: $x_i = 2 + i \cdot \Delta x$.
• Column C: $f(x_i) = \sqrt{3 \cdot x_i}$.
• Column D: $f(x_i) \cdot \Delta x$.

Finally, sum up the values in Column D to get the approximate integral.

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General Formula for the Approximation:

$\int_2^4 \sqrt{3x} \, dx \approx \sum_{i=1}^{11} f(x_i) \cdot \Delta x$ Where $x_i = 2 + i \cdot \Delta x$ and $f(x_i) = \sqrt{3x_i}$.

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Result:

After performing the computation in a spreadsheet, copy-paste your result directly here for submission.

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Would you like detailed guidance or specific formulas for setting this up in Excel or another tool?

Related Questions:

1. What are the steps for computing a left Riemann sum?
2. How does increasing the number of rectangles affect the approximation?
3. What is the difference between a right and midpoint Riemann sum?
4. How do you find the exact value of the integral analytically?
5. How can you automate Riemann sums for various functions in a spreadsheet?

Tip:

For best accuracy, ensure your spreadsheet uses enough decimal places in its computations to meet the $10^{-7}$ precision requirement.