# Riemann's Rookie Recruit

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#### Storyboard Text

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• ﻿Good Morning Class! Please start by opening up your grammar and writing books, remember to use pen....﻿﻿﻿﻿
• ﻿﻿﻿English 3 HonorsMs. Stapleton's ClassTo-Do- Grammar Pages 131-135- Turn in HW Assignment
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• ﻿﻿How do I integrate again.... what's the integral of x^-1... hmm... OH! ln(|x|), duh....﻿
• ﻿﻿﻿Ugh, I's failing Mr. Tipping's class so bad... I need someway to get extra credit﻿
• ﻿﻿﻿Hey, you, back to your seat...
• ﻿﻿﻿﻿﻿English 3 HonorsMs. Stapleton's ClassTo-Do- Grammar Pages 131-135- Turn in HW Assignment
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• ﻿﻿﻿﻿I hope this is a serious question, I have to get my homework done before next period starts! ... What's the integral of sin again? Oh right, negative cos..
• ﻿..WAIT! I got it!.. Hey, Valentina, aren't you in AP Calculus or something?﻿
• ﻿Oh, yea I am.. why do you ask? ﻿
• ﻿﻿﻿﻿﻿﻿English 3 HonorsMs. Stapleton's ClassTo-Do- Grammar Pages 131-135- Turn in HW Assignment
• ﻿What's a rhetoric..﻿
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• ﻿Oh, okay, sure If you want.
• ﻿﻿﻿Might as well teach her Riemann's sum, since it's what my homework is on anyway...﻿
• Wait, underneath a curve? Woah, I didn't even think that was possible!
• ﻿﻿Sooo, what's this ﻿Rheumatoid that you speak of?
• ﻿﻿﻿﻿﻿﻿﻿Oh, well it's simple, you're basically calculating the area underneath a curve, similarly to finding the area of a shape.
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• ﻿﻿﻿﻿﻿It's really simple! All you have to do is find your delta x factor, plug in your wanted coordinates, and you get an approximation of area!
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• ﻿Dissection
• Okay, so I'm going to need an example of this in action.﻿
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• ﻿﻿Sure! Here's how you would set up a Riemann's Sum problem
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• ﻿﻿﻿﻿﻿﻿﻿Now that you've found your delta x, divide your x-coordinates by the delta x and pick the values you desire (left, right, midsum, trapezoidal)
• ﻿﻿﻿﻿﻿So first you write out the equation of the line (x+3), along with determining how many equal-width rectangles your going to use...
• ﻿﻿﻿Next, find delta x by dividing your "b" (2) and "a" (1) by the number of rectangles (4) which gives you (1/4)
• ﻿﻿﻿﻿﻿﻿Lastly, plug all your chosen increments into the function and add them all up! To complete the approximation, you multiply by your delta x!
• ﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿1. x+3, n=4 on [1,2]2. delta x = (1/4)3. (4/4, 5/4), (5/4, 6/4), (6/4, 7/4), (7/4, 8/4)4. Lefties: 4/4, 5/4, 6/4, 7/45. {f(1) + f(5/4) + f(3/2) + f(7/4)]6. (1/4)(4 + 17/4 + 9/2 + 19/4)7. (1/4)(35/2)8. Left approximation of 35/8, or 4.375