Definition of Area Riemann Sum Limit of Sums Part 2 of 2 Calculus 1

I introduce the Definition of Area of a Plane. This is a special case of Riemann Sums where the width of the rectangles used to find the area of a plane bound by a function and the x-axis are all of equal width. Many examples are worked through.

[profrobbob]

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[profrobbob]

You are welcome:) If you keep watching my videos you will see that I try to wear a lot of math related funny shirts:D Thank you for watching and supporting my channel!

[profrobbob]

I'm glad you understand now and you're welcome! As a classroom math teacher too, I can confirm that it's hard not to be grumpy some days:( After watching a few more of my videos you should be able to go into class and teach them a thing or two...that should put a smile on your teachers face:))

[profrobbob]

You are very welcome...and thank you for choosing my video to watch and learn from!

[Felfor]

Thank you so much for this! I'm so sick of listening to my old grumpy math teacher, but now I finally understand thanks to you :)

[profrobbob]

If you don't specifically need to find the lower or upper limit, you can use the same corner of each rectangle to estimate the area under the curve. I chose to let the function define the upper right corner of each rectangle to simplify the work a bit. Lower bound of a closed interval which you finding the area of is not the lower limit.

[profrobbob]

NO...THANK YOU for watching and the nice comment:D

[arbihirchi]

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[BurritoBalladBBd]

You sir are a scholar and a saint. Thanks.

[profrobbob]

i starts with 1 in the sigma notation so you will need to do i-1 if you want to use the left side of the rectangle because you don't want to move off your lower bound for that first rectangle.

[profrobbob]

In your Ci equation you would have 0+(2/n)(i-1). This will complicate your algebra as you work through your limit process. If you were only using a few rectangles to estimate the area your answer would be different, but since you are letting the number of rectangles reach Infiniti your answer will be the same.

[connerross]

Common denominator is the bane of my existence in calculus lol everytime I have to use it in a problem I literally stare at it for 10 or 15 minutes confused as to how they multiplied the other one by a variable or a number and then it hits me. Honestly it seems like the hardest part of calculus besides optimization is just remembering all of the old algebra rules that you were taught 5+ years ago. Thanks for posting videos like this ProfRobBob you're a great teacher.

[profrobbob]

If the graph you are finding the area under has a positive slope you would find the lower sum by using the upper left corner of the rectangle and if the graph has a negative slope the lower sum would be found by having the upper right corner of your rectangle defined by the graph. If this does not answer your question, can you refer me to the time in the video you are asking about?

[profrobbob]

Meant to vote UP!!!!...stupid buttons!
Anyway...I'm so proud to see that you were paying enough attention to even comment from my shirt...BRAVO to my A+ on-line student...and Thank You for saying so:)

[ryanchishti]

Thank you so much for your help, you are helping me understand the lessons I am taught in university math.

[charliepace]

thanks :)


by the way, you are wearing a nice T-shirt sir.

[nobazter]

5/4 people think your the best math teacher

[blazethecat]

Sir can you help me with my assignment what is the definition of Area?

[mosscreature]

At 6:37 you say delta n instead of saying delta x