I Impressed My Boss With THIS Solution 💰

In this video, I show you how this definite integral can be a real world example of impressing your boss with some calculus 2! Integration tactics are important on your ap calc bc exam and by the end of the video, my hope is you'll use the ninja tricks you learned to quickly ace problems like this!
For this problem, we are given info that the definite integral equals 4, and so we need to figure out the upper limit of integration, n, that satisfies this equation. We'll use some algebra here by factoring the numerator and finally solving a resulting quadratic function to get the answer!
If you need a refresh on how to solve definite integrals, check out this video!
• This Quick And Easy Me...
0:00 - Intro
0:27 - Factoring The Numerator
0:42 - Breaking Up The Integral
1:12 - Evaluating The Integrals

[@NumberNinjaDave]

It can be frustrating wondering if you'll ever use calc in real life. Can you think of a time where YOU might get to use it?

[@ml09394]

Students: I will never use calc or the quadratic formula in real life
Number Ninja: nuh uh

[@NumberNinjaDave]

@@ml09394 hahaha, facts

[@DanDart]

Honestly I would recommend completing the square.

[@NumberNinjaDave]

Feel free to!

[@doraemon402]

0:40 You can't just do that without mentioning the fact that the integration interval may contain 1, which isn't defined but doesn't change the integral because the value of the two functions is the same "almost everywhere", in this case, everywhere but 1 point, which has zero measure.

[@NumberNinjaDave]

@@doraemon402 remember that for limits, what matters is that you don’t have jump discontinuity at a point and note what the fundamental theorem of calculus says.
You are correct though when talking about the domain of the original differential

[@undead_donut6468]

2:30 you can just skip the whole quadratic formula by factorising to (n+4)(n-2) = 0 which gets you n = 2 as n cannot be negative.

[@NumberNinjaDave]

Great observation! You truly are a 🥷

[@undead_donut6468]

also would love to have a boss like this lol

[@NumberNinjaDave]

Hahaha that would be epic

[@archangecamilien1879]

Lol...=n...

[@NumberNinjaDave]

@@archangecamilien1879 watch the video tomorrow to see if you’re correct

[@teerthpaliwal727]

Shouldn't the answer be 3

[@NumberNinjaDave]

@@teerthpaliwal727 no

[@NumberNinjaDave]

@@teerthpaliwal727 (1/2)(3^2) + 3 = ?

[@teerthpaliwal727]

Oh ryt, sorry I literally forgot abt integrating, I just did the (x + 1)(x -1 ) / (x - 1) ... Im sorry, my mistake, thanks for correcting:)

[@NumberNinjaDave]

@@teerthpaliwal727 all good 🥷