Calculating a Definite Integral Using Riemann Sums - Part 1

Calculating a Definite Integral Using Riemann Sums - Part 1.
In this video, I show how to set up a definite integral using Riemann Sums. In part 2, I actually compute the Riemann Sum to get a solution!
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Category:

Education

Tags:

• math
• calculus
• riemann
• sum
• reimann
• example
• integrate
• integral
• derivative
• summation
• formula
• integration
• SAT
• BC
• AP
• ACT

[ronniemonnie]

Why do we use the formula a + (delta x)i to calculate xi*?

[patrickJMT]

@ronniemonnie well, label points on the number line: x_0, x_1, x_2, etc and find a formula for their values.

[Slappydappy]

What exactly does "x of i star" in this video represent? The way it's calculated is giving me the right interval point of the rectangle.

[patrickJMT]

@Slappydappy it represents any point in the ' i-th ' interval. the idea is that you really do not have to use left endpoints or right endpoints in the definition; all that is needed is to take a point from each interval. the x-i notation is pointing that out.

[Slappydappy]

@patrickJMT If your calculating an Integral don't you need to use midpoints? Or does it not matter?

[patrickJMT]

@Slappydappy if you are approximating an integral, you can use any point in the interval. to prove that an integral can be calculated by antiderivatives, it turns out you can again use any point in the interval.

[fremsley001]

You can also calculate definite integrals by drawing the function as a curve on a piece of grease-proof paper, filling the area underneath with a uniform layer of cream cheese, then carefully scraping it off and weighing it on kitchen scales, giving the answer in "Philadelphian equivalents." This is the way Riemann himself did it before he hit on the idea of his sums. (PS. Andrew Wyles used cough drops and teaspoons to prove Fermat's Last Theorem.)

[patrickJMT]

@fremsley001 that is f-in hilarious

[halospartan5]

This guy probably got laid every night in college. He makes this shit look so easy

[HaydnM35]

MARRY ME

[TheBright01Star]

thanks you made it so simple =D

[dala555]

this seems like an overly complicated way of doing something very simple.

[legoindianajones1000]

@kdizzle20901 yes

[legoindianajones1000]

Can reimann sums be used without a function, just points on a graph? Let's say I have 30 points on a graph, to calculate the area, will I have to do middle,right, and left endpoints to get it? Or can I use reimann sums?

[TearfulCar1]

so much better now!!!!! Thank X1000000000000

[Alandar2030]

great! thank you. I finally understood this crap! God bless.