The Definite Integral - Understanding the Definition

The Definite Integral - Understanding the Definition. In this video, I discuss the definition only; I do not calculate any definite integrals.

Category:

Education

Tags:

• calculus
• definite
• integral
• definition
• indefinite
• riemann
• sum
• reimann
• integration
• limits
• area
• under
• curve

[iSlapHoesOnUtube]

im paying so much money for my college tuition yet i dont get anything my professor says. i watch your videos for free and i get it. why dont i just pay you? the education system is messed up

[patrickJMT]

@iSlapHoesOnUtube i accept checks and cash : )

[MrOverdoseXL]

I love this! So clear. :)

[patrickJMT]

@MrOverdoseXL perfect! : )

[snarejaguar1]

would you find xi* by doing (a + deltax times i) ?

[patrickJMT]

@snarejaguar1 yep, that is exactly what you do. you that when finding the exact value of a definite integral using the definition.

[backcountryjame]

thumbs up for left handed people!

[therock343]

WOOOWW... 2 hr Confusiing Lecture vs. 9 min Clear and simple Video.. Omg.. I love you Man! All Homo! haha

[CallOFDutyMVP666]

I find it amazing that you can add up an infinite number of infinitesimal cross sections and get a finite value.

[MrHishmeister]

This is exactly why I dont go to class :D !!! Patrick rules !!!!

[andr00123]

@andr00123 Well that was a mess... sorry guys :( hope you get it.

[andr00123]

Find area of ƒ(x)=x^3 between x=0 and x=1 ∆x = 1-0/n = 1/n and Xi=0+i(1/n) so, ∫(x^3)∂x = lim ∑ (Xi^3)∆x = lim ∑ (i/n)^3 (1/n) <---replaced Xi with i/n and ∆x with 1/n = lim ∑ (i^3/n^3)(1/n) = lim 1/(n^4) ∑ i^3 <--- 1/(n^4) taken out so sum can be put in terms of n = lim (1/(n^4))((n^2(n+1)^2)/4) = lim (n^2 + 2n + 1) / (4n^2) <--- skipped steps to simplify (basic algebra) = 1/4 Why 1/4? Notice how the top power on both parts of the fraction are equal. Old property of a limit in Cal I

[andr00123]

@jokerarayko n is the number of separations, or delta x's. When you find the true area using the limit, n is approaching infinity. The trick to solving the Riemann sum is to take the value's "n" as a constant (so that it looks something like this example: 2/n∑i). After solving the sums, you will be left with "n's" in a fraction. The numerator and denominator should have equal powers of n. The second part of this comment will include an example

[fistful0fst33l]

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[jokerarayko]

How do you determine n?