Welcome to Clip from Spiral logo

Interactive video lesson plan for: How do you convert a Riemann sum to a definite integral? (KristaKingMath)

Activity overview:

0:25 // Definition of the Riemann sum
0:50 // What you need in order to use a Riemann sum to find area
1:09 // The difference between a Riemann sum and an integral
1:34 // Converting a Riemann sum into a definite integral
2:09 // Converting an example Riemann sum into a definite integral
2:35 // Summarizing how to use the Riemann sum versus the definite integral

We know that Riemann sums estimate area, and we know that integrals find exact area. But how do we convert a Riemann sum into a definite integral?

The simple answer is that we just use an infinite number of rectangles to find the area, instead of a finite number of rectangles, like we normally would when we're using a Riemann sum. If we want to express the fact that we're going to use an infinite number of rectangles, we need to add a limit out in front of the integral as n (the number of rectangles) approaches infinity, and then the Riemann sum has become a definite integral.

As long as we know the interval over which we're trying to find area, we can change the limit and summation notation into integral notation, with the limits of integration reflecting the interval we're interested in. We change the function f(x_i) into a function f(x), and we change the delta x into dx. And that's actually all it takes to change the Riemann sum into a definite integral.

Music by Joakim Karud: http://soundcloud.com/joakimkarud

● ● ● GET EXTRA HELP ● ● ●

If you could use some extra help with your math class, then check out Krista’s website // http://www.kristakingmath.com

● ● ● CONNECT WITH KRISTA ● ● ●

Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student—from basic middle school classes to advanced college calculus—figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: http://www.kristakingmath.com

FACEBOOK // https://www.facebook.com/KristaKingMath
TWITTER // https://twitter.com/KristaKingMath
INSTAGRAM // https://www.instagram.com/kristakingmath/
PINTEREST // https://www.pinterest.com/KristaKingMath/
GOOGLE+ // https://plus.google.com/+Integralcalc/
QUORA // https://www.quora.com/profile/Krista-King

Tagged under: Krista King,area approximation,convert definite integral,educational,area estimation,definite integral,convert,converting,integral,riemann sums,convert riemann sums,calculus,estimating area,approximating area

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share How do you convert a Riemann sum to a definite integral? (KristaKingMath) on Google+ Share How do you convert a Riemann sum to a definite integral? (KristaKingMath) on Twitter Share How do you convert a Riemann sum to a definite integral? (KristaKingMath) on Facebook Pin How do you convert a Riemann sum to a definite integral? (KristaKingMath) Email How do you convert a Riemann sum to a definite integral? (KristaKingMath)

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Spiral
Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Spiral
Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Spiral
Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome