Riemann Sums - Midpoint, Left & Right Endpoints, Area, Definite Integral, Sigma Notation, Calculus

[@TheOrganicChemistryTutor]

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7:00 width (delta x) formula, interval (no. of rectangles), points (x) MIDPOINT approximation

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[@brenmclean]

At 9.14, the Area (Left) is calculated to be 3.25. You then use 3.75 later. Also, my textbook defines the average Area of Left plus Right (1/2 L + R) as the Trapezoid Rule.

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At 56:17 you are doing a sigma notation problem and you’re trying to simplify all n. When you cancelled n^3 shouldn’t there be a 2/6 left over? I think you ignored the 2 and just got rid of it.

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55:13 What would I do is: Transfer 6 to the place of n^3, and transfer n^3 to the place of 6. Then we see that 27/6 is a constant, so using the limit property, we take that constant outside the limit. So now we left with the 27/6 times limit of (2n^3 + 3n^2 + n)/n^3. Use a well-known shortcut (consider one term with the highest power in the numerator and one term with the highest power in the denominator), so lim of 2n^3/n^3 = 2. And remember we have a constant. So 27/6 * 2 = 27/3 = 9. instead of shortcut above you can use even faster shortcut: if the highest power in the numerator equals to highest power in the denominator, then the lim will be the ratio of their coefficients.

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[@islombekabdurahmonov1115]

MISTAKE: LEFT = 3.75. BUT YOU USE 3.25 WHEN CALCULATING AVERAGE OF A(L) + A(R)/2 in 15:23.

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[@user-px1wj2uv3r]

There's a mistake on problem 1. A sub L = 3.75, which you did get initially but wrote 3.25 when averaging. So the avg of A sub L and A sub R = 4.735.

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[@nischalshrestha5443]

At 14:08 , the area of the left end sum was 3.75 not 3.25

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