This video is more complicated than it needs to be. When you substitute the "1/2x" into the integral you'll have "x/2x" the x will disappear and you'll be left with "1/2" and since it is a multiplier you just bring the one half outside of the integral. This is a lot more simple than multiplying by two and one half to keep the integral the same in order to have a "2x/2x".
Sorry, I have a Masters in both Business Admin and Accounting. I took AP Calculus AB and BC in High School but didn't have to in college. I am always looking to improve myself so I am trying to learn new things; such as refreshment on calculus and physics topics.
Well often this would be only a very small part of a larger application, not all things can by it self be directly applied. I truly get how we want things to have a direct application, but sometimes one simply needs to take a leap of faith and try to learn the theory and realize than unless one wants to go into plumbing and construction, some times things will get abstract :)
@@pram5532 An integrand is the result from basically converting an integral back into a higher-order function. An integral is the same as getting the derivative of whatever higher-order function you started off with. For example: an integral, like 2x, is what you get after differentiating x^2. They are opposites of each other.
I suppose everyone is entitled to their opinion; which is why I expressed mine. I like that integral calculus has uses. I was simply suggesting that before or perhaps during the explanation of the technique being taught that use of technique in a real world example would be helpful. If I hand you a tool and fail to teach you what it can be used for, I am relying upon you to figure out how to use it. Sure, eventually I may figure it out but it's faster to teach me up front what it is used for.
hi. i have a feeling you should write the 'd' properly, otherwise people could get confused later with partial differential equations where the d's are written more curly like in your vid... just a thought.
I was an award winning teacher--in the fourth largest district in the United States, I harnessed the power of technology to take my students to places they have never been! I provided implementation ideas to my school and the children really benefitted. More power to you! By the way, "Giving Our Students the World" is my motto and it is now the motto for ~ 400,000 students. So, yes, I AM a caring teacher--that's my philosophy.
I freaking HATE integrals. I am litteraly never going to use them in my entire life and I am forced to learn them. Plus to make things worse, every person I watch who is calculating integrals does it completely different somehow. Jus out of the blue every time...
You will be faced with problems in life. You will be forced to solve them. If you can apply logic and reasoning to solve problems in mathematics, you can transfer those skills into other areas of life.
try showing an example of substitution when you cant use the u' straight on ...these are type "Oh look at that how lucky am I there is u' sitting right next to my u"...
Wow. I really need to go back to college. Two master's degrees and I still don't understand the application of this math. What would I even use it for? These videos could be significantly enhanced by starting with a real-world use so that I can start integrating the knowledge by seeing it in context. Then I could understand how the components fit together. Math for math's sake is dry; even for someone who loves learning new things.
Mathematics IS a real world. You use substitution to do integrals. E.g. it can reduce a wide range of trigonometric integrals to rational integrals. Among other things.
Would you mind stating the area of your academic studies? I mean no disrespect, I'm just appalled to realize that teachers at post-graduate level can avoid explaining the huge real world impact of basically any branch of calculus.
obviously you haven't paid much attention during class, integrals are used to solve,max-mini equations, in fysics, for calculating the area under a curve, it s used extensively in economics alongside with derivatives.... my man if only you would take the time to have a greater look in to every practical thing around us, you would quickly realize that 90% is built upon math... so not math for math s sake is not dry. it s all around us...
By the way, I remember calculus, but the thing that brought me here was Nightline. The One World School book sounds like it is perfectly aligned with my philosophy--a must read for me. Great job, my friend--and I, too, have an M.B.A. but taught children out of love.
"Math for math's sake is dry; even for someone who loves learning new things." Pure mathematicians like G. H. Hardy would strongly disagree. Besides, integral calculus is used in areas like electromagnetism, and by extension electrical engineering.
