Use four rectangles to find an estimate of each type for the area under the graph of $f (x) = \sqrt{2 x}$ from $x = 0$ to $x = 4$ .
1. Take the sample points from the left-endpoints.

Answer: $L_{4} =$
2. Is your estimate $L_{4}$ an underestimate or overestimate of the true area?
Choose one
3. Take the sample points from the right-endpoints.

Answer: $R_{4} =$
4. Is your estimate $R_{4}$ an underestimate or overestimate of the true area? Choose one
5. Take the sample points from the midpoints.

Answer: $M_{4} =$

Answer

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Answer

$L_{4} = 5.863703305156273$

Steps

Step 1 ：Divide the interval [0,4] into four equal subintervals with a width of $\frac{4 - 0}{4} = 1$

Step 2 ：Calculate the function value at the left-endpoints $x = 0, x = 1, x = 2, x = 3$ using $f (x) = \sqrt{2 x}$

Step 3 ：Find the area of each rectangle by multiplying the function value by the width

Step 4 ：Sum up the areas of all four rectangles to get $L_{4}$

Step 5 ： $L_{4} = 5.863703305156273$