MAT 211 Chapter Notes - Chapter 4: Antiderivative, Mean Value Theorem, Equipartition Theorem
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12 + 22 + 32 + + n2 = n (n + 1) (2n + 1) 13 + 23 + 33 + + n3 = n2 (n + 1)2. There are three di erent ways to determine the sum of the triangular heights. Also, if you let x be a sample point in the ith interval, then the following inequality would be proper: i. Then, the ith rectangle would be the following: xi 1 x i xi. Therefore, the approximated area that would be the area that"s under the curve thanks to adding the areas of the rectangles, which can be written as the following: a n. Then the sum of the left-hand sum and you would get the following: x i = xi 1. A ln (f ) = f (xi 1) x n. Then the sum of the left-hand sum and you would get the following: x i = xi.
