Thankyou so much for your explanation about Riemann Sums. Very well explained! And btw, is my answer correct at 22:12, 1) (e^2-1)/2 = 3.1945 2) 1 3) 2(sqrt(27)-1)/3 = 2.7974
My professor from Romania used to give these to us! At the time, there were very few resources that covered this topic (most were older) so we had to figure out what the hell was going on by ourselves LOL They are good exercises for checking to understand you know what an Integral means, at least in Riemann's definition of the integral which is probably the easiest and more practical. I love these exercises! Even today, I see someone post these on Twitter and usually no one knows how to tackle these or they say it's 0 (even someone with a PhD in physics was baffled by this), so it's definitely not something I think most curriculums teach anymore. Well done on the video and thank you for demonstrating this!
When it comes to Riemann sums, i prefer to actually put it at the side’s midpoint, as it gives a better approximation. If you were to rotate the protruding part of the rectangle π radians about the midpoint, it would better match the graph
1st exercise: You were right: 2(i/n) is not a typo. Delta X = dx =(2/n). f(x) = (1/2)e^x. Answer: (1/2)(e^2-1) 2nd exercise (Edit form 12/10/2023 and FINAL): You made a typo and I made a typo because n-term is (π/2)(1/n)cos(nπ/2n). Xi= 0 + (i/n) Δx = dx =1/n f(x) = (π/2)cos(πx/2). Answer: (STILL) 1 (Retract all their answers, please. Im right and I proved it is right three times) 3rd exercise: Delta X = dx =(2/n). f(x) = √x. Answer: 2√3-(2/3)
@@santiagoarellano6434 you both have different end points because he interpreted as it an integral from 0 to 2 while you have found a function for which the interval is 0 to 1 ( do you have (1/2)e^2x as the integrated function or the unintegrated function cause there might be a mistake in your reasoning)
Your second answer is wrong as the sum goes up to 2n instead of n because you can see the last term in the sum on the board is cos(nπ/n) = cos( 2n π/2n) so the integral is from 0 to π instead of from 0 to π/2. final answer is 0
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got a test in 3 hours but now i'm more confident I CAN'T THANK YOU ENOUGH
Glad to hear! Hope u did well!
@@bprpcalculusbasics thanks i did good! 😭
I like your channel. Kindly prove fundamental theorem of integral calculus.
2:25 i love how he doesn't cut anything out
Thankyou so much for your explanation about Riemann Sums. Very well explained!
And btw, is my answer correct at 22:12,
1) (e^2-1)/2 = 3.1945
2) 1
3) 2(sqrt(27)-1)/3 = 2.7974
I think the answer to the second question is zero
@@quasbhop3790No, it's 1
On 3) you could simplify √27 to 3√3
@@SnekoyIt's 0
answer to the questions
1) (e⁴-e²)/2
2) 1
3) ( 3sqroot3-1)/2
please cross check
15:48 Answer: 39
The total number of integers between 0 and 10^5 having the digit sum equal to 8 is n then find 5(500 - n). pls answer my Question...help me solve this
1675 ??
I like your funny words magic man
My professor from Romania used to give these to us! At the time, there were very few resources that covered this topic (most were older) so we had to figure out what the hell was going on by ourselves LOL They are good exercises for checking to understand you know what an Integral means, at least in Riemann's definition of the integral which is probably the easiest and more practical. I love these exercises! Even today, I see someone post these on Twitter and usually no one knows how to tackle these or they say it's 0 (even someone with a PhD in physics was baffled by this), so it's definitely not something I think most curriculums teach anymore.
Well done on the video and thank you for demonstrating this!
In my feed one third of video recommendation comes from your channel
👍
Same here
How to tell that you are intelligent without telling...
Can someone tell me in which account He explain about Trapezoid Method and Newton Method (gradient one IIRC)
example 4 would look even stranger if you would have divided n^2 in the numerator by the external 1/n.
When it comes to Riemann sums, i prefer to actually put it at the side’s midpoint, as it gives a better approximation. If you were to rotate the protruding part of the rectangle π radians about the midpoint, it would better match the graph
is the answer 1/2 (e^4 -1)?
Super hot is not a pew die pow rapper 😅
07:40
the answer of the integral of x^2 starting from 2 and to 5 is 39.
Thank you
Love your t-shirt -!!❤❤🎉
I don't think there is a nerdier t-shirt than that, I want it.
thanks for help
square roots of x = x - 2
why can't we take square on both side
x just cant equal x-2, take square on both sides if u want you still wont get an answer
Hmm
1st exercise: You were right: 2(i/n) is not a typo. Delta X = dx =(2/n). f(x) = (1/2)e^x. Answer: (1/2)(e^2-1)
2nd exercise (Edit form 12/10/2023 and FINAL): You made a typo and I made a typo because n-term is (π/2)(1/n)cos(nπ/2n).
Xi= 0 + (i/n)
Δx = dx =1/n
f(x) = (π/2)cos(πx/2).
Answer: (STILL) 1 (Retract all their answers, please. Im right and I proved it is right three times)
3rd exercise: Delta X = dx =(2/n). f(x) = √x. Answer: 2√3-(2/3)
Would you be so kind as to elaborate on your reasoning for answer 1?, I tried it myself and got (1/2) e^2x instead of just e^x
@@santiagoarellano6434 te contesto en inglés o en español?
@@santiagoarellano6434 Check Example 2. I used the same reasoning
@@santiagoarellano6434 you both have different end points because he interpreted as it an integral from 0 to 2 while you have found a function for which the interval is 0 to 1 ( do you have (1/2)e^2x as the integrated function or the unintegrated function cause there might be a mistake in your reasoning)
Your second answer is wrong as the sum goes up to 2n instead of n because you can see the last term in the sum on the board is cos(nπ/n) = cos( 2n π/2n) so the integral is from 0 to π instead of from 0 to π/2.
final answer is 0
Hi Sir....love from India....
hello
In India this is a standard example of definition of integration
DEFINITION please.
This is also an example in every other country