When the points x i ∗ are chosen randomly, the sum ∑ i = 1 n f ( x i ∗) Δ x i is called a Riemann Sum and will give an approximation for the area of R that is in between the lower and upper sums. The upper and lower sums may be considered

Math AP®︎/College Calculus AB Integration and accumulation of change Approximating areas

Solved Examples Using Riemann Sum Formula Example 1: Find the area under the curve f (x) =

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Riemann Approximation Step 1: . Find out the width of each interval. Step 2: . Step 3: . Define the area of each rectangle. Step 4: . Let’s say the goal is to calculate the area under the graph of the function f (x) = x 3, the