Problem

Approximate the area under the curve graphed below from $x=1$ to $x=6$ using a Left Endpoint approximation with 5 subdivisions.

Solution

Step 1 :Define the function that represents the curve. For this demonstration, let's assume the function is \(f(x) = x^2\).

Step 2 :Define the interval [a, b] and the number of subdivisions n. In this case, a = 1, b = 6, and n = 5.

Step 3 :Calculate the width of each subdivision. This is done by the formula \(\delta_x = \frac{b - a}{n}\). For this problem, \(\delta_x = 1.0\).

Step 4 :For each subdivision, calculate the left endpoint and find the function value at this point. This is done by the formula \(x_i = a + i * \delta_x\) and \(f(x_i)\).

Step 5 :Multiply the function value by the width of the subdivision to get the area of the rectangle.

Step 6 :Sum all the rectangle areas to get the total area under the curve. The total area for this problem is 55.0.

Step 7 :Final Answer: The approximate area under the curve \(f(x) = x^2\) from \(x=1\) to \(x=6\) using a Left Endpoint approximation with 5 subdivisions is \(\boxed{55.0}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8782/

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