Approximate the area under the curve graphed below from $x=1$ to $x=6$ using a Left Endpoint approximation with 5 subdivisions.
Answer
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 \(\boxed{55.0}\).
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 \(\boxed{55.0}\).
