Anybody who said THIS was the simpler approach(compared to the prior vids.) was clearly baiting you into flexing your mathematical mind. And for that, i thank them. I'm doing some math related academic upgrading, and your videos are the first math related ones I've begun enjoying. Thank you for that.
@syed3344 yep i agree this is some elementary integral, i follow along the video not knowing the initial solution and when i see it at the end of the video my mind went “damn its just 2 quarter of circle and a smol square”
Me being jee aspirant of 12th standard can confirm that yes we do this kind of questions a lot in chapter application of integrals😅 Btw it was not difficult but just lengthy and satisfying after getting an answer
I'm from Brazil. Although I studied calculus a bit for my college degree (Economics), I've never studied or used it again for decades. Your channel has been a fun and educational ride thru the memory lane. Keep up with your marvelous work.
I’m from California, I’m currently wrapping up the Calculus course triathlon at my school after taking a semester’s worth of a break. I wanted to save some videos to get me back into this subject and your channel has been one of the best ones by far!
I'm from Ohio, USA. My wife is a 7-12 math teacher. The Algorithm brought me to your channel and I was so excited to share your content with her. I'm >20 years out of school and never took a math course more advanced than Calc II but I absolutely love math (I should have at least minored in math, in retrospect). We both enjoy your content very much. Thank you for these posts - they're always fun to watch, especially when you take a different approach than I would and it gives me new perspectives.
Chile! I watch your videos till the very end. It's very satisfying to see the end result and hear your "how exciting". Your explanations are clear and straightforward, I love their minimalistic style.
I love you and your context Andy! Keep it up! I did have a question- how did you get into math, and what’s your education level/occupation? (PS, Texas)
I’m from Thailand. I have been watching your videos for months and really love it. This calculus approach is fantastic and definitely easier for someone like me, who is completely comfortable with graph and integration because the geometry ways are too much for me. Keep up the great work!
I'm from Asia! I found this channel a few months ago about a geometry question, and this channel has really sparked my interest in mathematics. Thanks Andy!
I'm from Philippines and currently studying integral in this upcoming semester. I am amazed on how you answer this problem for several times and also I love all of your geometry problems.
Hello from Scotland :) Love the videos, always perplexed looking at the problem before the explanation, then in awe watching you solve it step by step :) I am not a mathematician but absolutely love the videos!
I’m From Egypt, I’ve always been fascinated by math and this channel only made it much more fun, I haven’t been on the level of grand calculus yet, yet your videos make it seem more fun than how some other aspects of learning maths would go by it. Your videos are awesome dude!
North Carolina, It has been 30 years since I touched calculus and I have forgotten a lot. I love your geometry videos and have used them a lot to help my children in school.
I’m a licensed chemical engineer here in the Philippines. It’s been exactly 10 yrs and 3 months since my graduation in College. Love seeing integrals and makes me want to review it again. INTECAL is my favorite math subject back then hehe
wow, I expected calculus to be faster at finding a solution for this, good job finding the u-substitution for the first integral (from Ukraine, living in the US)
after you found the area under the green circle .. you can multiply it by 2 to get the similar section under the second (blue circle) and then add the red square (where X is placed on the graph) its area should be 5x5 .. a faster shortcut to same answer 🙏 well done .. love your videos❤️
India! Miss the time I used to solve calculus questions like a boss during my undergrad! Had stumbled upon this page randomly and it's kinda nostalgic to see all this now after almost a decade! Bet I'm the lone few who are happy seeing calculus! Cheers.
I'm from Colorado. I've always loved and excelled at math, but I've let myself stagnate in the last 10 years. Your videos are reawakening the passion and interest I used to hold!
Fairview, TN. Andy, your videos are terrific. I aced algebra, trig, and geometry in HS, but I never had calc. Got to engineering school in college and both calc and dif eq crushed me. Listening to you has lecture helps me see some logic in calc the same way i saw it in my HS mathematics courses.
Stephen from NC. Thanks for this video. I’m slowly starting to understand it and I take Calculus 1 in the fall. Yours and several others videos are really helping!!!
I'm from South Africa, currently studying my masters in Industrial Engineering. I came across your channel on TikTok, and it led me to your YT channel. U make maths problems look easy I must say
enjoyed that a lot, although I don't know enough to follow 70% of it going to go watch the other videos on the same problem shortly from Texas, living in Japan
I’m from India , and I am studying for IIT , whenever I am bored (from chemistry ) I just come to see your videos and freshen up. These videos are actually really fun to watch them them step by step and the level of questions is quite good (challenging) and you just make them so easy .
How are the papers these days? Tough? Easy? Back when we were preparing, our standard set was 1996-2004 papers. What's considered the "standard" set these days?
I really don't know how integrals work but I liked this video. The way you solved it was really clean and if i knew the properties of integrals i would've understood it without even needing to pause the video.
I’m from the UK, and now nearly 30 years out of college. I was a maths and engineering major, and always loved the simplicity of geometry… and hated calculus! I love the videos and frankly don’t know how you get the ideas to put together. Well done!!
I am from Bangladesh and I recently finished by A Levels. Find out abut channel only recently, this videos stuck out to me since I was doing solving similar problems w/ calculus in my Pure Mathematics course.
I love your content, geometry is just fascinating and your approach is so inviting. Do you have any recommendations for textbooks or resources for people out of school but who like geometry? (From Saskatchewan, Canada!)
Wow! That was really nicely done. I made it to the end......I'm a college math teacher from Hopkinsville, KY (and love your channel!....I've shared several videos with my colleagues). One question though.....once you found the first area under the circle, couldn't you have noticed that would be the same area under the second circle plus the square area and "finished" a little easier.......or did you want to use calculus for the entire problem. Either way, well done!
Excellent one! Here from Argentina, really wanted to go through all the video although you could have "cheated" by stating that the second part was the area of the first part plus the square below... But you proved it also with the sustitution, so kudos!!! Thank you very much!!!
you can actually halt the calculus after finding the definite integral of the green square 0 to 5. because you can see that the red shaded region is symmetrical along the (10,0) , (0,10) diagonal. so simply add the area of the 5 by 5 right triangle to the green circle's integral you calculated... and then double the result to complete the symmetry of the red-shaded region.
In college, even though my degree didn't require it, I wanted to learn calculus. I wanted to be a guy who "knew calculus". I started taking math classes working in that direction, but required classes took priority and I never ended up taking any calculus classes. Later I started working through online classes, but got busy and didn't finish. I bought a calculus text book and didn't get very far in that. Well. I just watched this video and...... I think I've now officially lost interest in ever learning it. That was crazy! I can't imagine how much work I'd need to put in to learn all that. (I guess I'm still interested, but can't imagine ever having the time or energy....) I'm from San Diego, btw. I love these videos, in a strange way, the way you take these challenging problems and break them down makes it feel like maybe my life's problems also have solutions.
I took calculus 3 years ago in highschool and ive almost completely forgot how to do most things in it. Ive now started working towards a computer science degree in which ill have some more advanced math classes so these videos are a great way to get back in the problem solving mindset.
