Welcome to Clip from Spiral logo

Interactive video lesson plan for: cU5L1c pt III LRAM MRAM RRAM Rectangular Approximations hand Riemann left right calculus

Activity overview:

For more cool math videos visit my site at or

Good day students will come two-part three on our rectangle approximations of now let's take a look at the instructions for the question we are to estimate the distance and object with a given time velocity chart covers in the first ten seconds of new movements using the left rectangular approximation okay so we are to use this time velocity chart provided right here to estimate the distance covered in the first ten seconds. So in what way are we going to use LRAM in this calculations so to do that lets take a look at some formulas first and then we can see the justification of our application of LRAM and the situation right so when connecting position velocity acceleration and jerk we talked about the savants continuum SB AJ representing position velocity expiration jerk away go down in this direction a differentiate in the anti-differentiate when going in the other direction okay so let's see what it is go from position to velocity how do you do that the have position of if you differentiate position with respect to time that gives you the velocity function right now what of if I wanted to get my position isolated how can I get position is a velocity as indicated in this the charts right here so let's start off by multiplying both site in this equation by DT okay and that yields DS equals the dt. Right so to get rid of that is the components were going to anti-differentiate so we're going to take the anti-derivative of both sides of the definite integral of both sides in the we going to have a cancellation action happening here is interval oriented derivative counsel that will the derivative on the left side will have the position S equals the integral of velocity the DT okay so the integrates the jerk function to get the expiration in the integrated solution function you get the velocity and if you integrate the velocity function you get skewed position function as indicated here right sell it way to find a position from 0 to 10 as indicated in this problem we going to calculate the definite integral from 0 to 10 of the velocity function right since we do not have a velocity function is going to be making an approximation as indicated in the problem is going to find the Valley of this definite integral using the left rectangular approximation okay from 0 to 10 right so what is LRAM let's go ahead and review that formula real quick in the search and its applicability to this situation, under consideration here okay so LRAM left rectangular approximation let's see we have X of an interval's it's going to be given by the with times F of the pick all the points to the left of the right endpoint okay so is can a look something like this the with times F of X one plus F of X to all the way to the X value before the right endpoint which we can in the case with X sub and minus one okay now you have to be really careful to note that this formula is for and equal sub interval's right and equal sub interval's now let's let's represent discharges in our interval notation interval chart and then see if we can use is from our here okay right so we can make an x-axis, interval this would help meet a certain my my my X my inputs into my LRAM formula okay so it does say this one is for over to the left a little bit right rights I have a number line, going to partition it from were going from zero all the way to eleven so let's say this is zero zero companies two boxes here case zero one two three four five six seven eight nine ten eleven rights is that's eleven so let me take a tour these numbers here pick up the one to take a look at so let's see where going from zero all the way to two I just want to put the numbers that show up on our chart here so don't get confused so the from zero two two and then from two two three and there from 3 to 6 four five six from 6 to 9 seven eight nine from 9 to 10 and there from 10 to 11 know what you notice about this interval that we have right here this is one interval this is another this is another interval is another interval

Tagged under: area,curve,estimating,finite,sum,average,dummy,variable,error bounds,Riemann,simpson' rule,sigma,upper,limit,bound,partition,norm,trapezoidal,region,definite,integral,integration,antiderivative,approximating,hand,left,LrAM,Method,numerical integration

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 cU5L1c  pt III LRAM MRAM RRAM Rectangular Approximations hand Riemann left right calculus on Google+ Share cU5L1c  pt III LRAM MRAM RRAM Rectangular Approximations hand Riemann left right calculus on Twitter Share cU5L1c  pt III LRAM MRAM RRAM Rectangular Approximations hand Riemann left right calculus on Facebook Pin cU5L1c  pt III LRAM MRAM RRAM Rectangular Approximations hand Riemann left right calculus Email cU5L1c  pt III LRAM MRAM RRAM Rectangular Approximations hand Riemann left right calculus

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.


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


Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices


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

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

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

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

Review of Spiral by teacher: Miss Ord @ordmiss

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

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

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

Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

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