Use the data below to calculate a right hand sum with 5 rectangles to approximate the area under $$ y=f(x) $$. $$ \mathrm{RHS}_{5}=[?] $$

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1. Identify the interval of integration. Suppose the interval is $$[a,b]$$.  
2. Compute the width of each rectangle as  
$$
\Delta x = \frac{b-a}{5}.
$$
3. The subinterval endpoints are  
$$
x_0,\, x_1,\, x_2,\, x_3,\, x_4,\, x_5,
$$
where $$x_0=a$$ and $$x_5=b$$.  
4. For a right‐hand sum the value used on each subinterval is the function value at the right endpoint. Thus, the area approximation is computed by  
$$
\mathrm{RHS}_5 = \Delta x \Bigl[f(x_1) + f(x_2) + f(x_3) + f(x_4) + f(x_5)\Bigr].
$$
5. Next, using the provided data (which should give the values of $$f(x)$$ at the endpoints), substitute:
   - $$f(x_1)$$ is the function value at the right endpoint of the first subinterval,
   - $$f(x_2)$$ is the function value at the right endpoint of the second subinterval, and so on.
6. Finally, multiply the sum by $$\Delta x$$ to obtain the approximate area under the curve $$y=f(x)$$.

Thus, the answer is  
$$
\boxed{\mathrm{RHS}_5 = \Delta x \Bigl[f(x_1) + f(x_2) + f(x_3) + f(x_4) + f(x_5)\Bigr]}.
$$

If, for example, the interval is $$[a,b]=[x_0,x_5]$$ and the data table provides particular numerical values for $$ f(x_1), f(x_2), f(x_3), f(x_4), f(x_5) $$, then substitute their values into the formula above to compute the numerical approximation.
To approximate the area under $$ y=f(x) $$ using a right-hand sum with 5 rectangles, follow these steps: 1. **Determine the interval**: Identify the start and end points $$ a $$ and $$ b $$ of the interval. 2. **Calculate the width**: Divide the interval into 5 equal parts by finding $$ \Delta x = \frac{b - a}{5} $$. 3. **Identify subinterval endpoints**: The endpoints are $$ x_0, x_1, x_2, x_3, x_4, x_5 $$, where $$ x_0 = a $$ and $$ x_5 = b $$. 4. **Compute the sum**: Use the function values at the right endpoints: $$ \mathrm{RHS}_5 = \Delta x \times [f(x_1) + f(x_2) + f(x_3) + f(x_4) + f(x_5)] $$ 5. **Substitute the values**: Plug in the actual function values from your data to get the numerical approximation. So, the right-hand sum is: $$ \mathrm{RHS}_5 = \Delta x \times [f(x_1) + f(x_2) + f(x_3) + f(x_4) + f(x_5)] $$

Use the data below to calculate a right hand sum with 5 rectangles to approximate the area under .

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