Calculus is fun when you understand it, but man I just can’t fully wrap my head around integration
Discussion
Integrel calculus is awesome if you self study and get it or if you have an amazing prof. I was not self motivated at the time and filed integrel calculus the first time. The second time around was by favorite instructor I ever had and I aced it.. he was a nutter and made it fun.
I’m using study . com and I’m about 2 hours from finishing the study material before I can take the final. I think I’m gonna have to study the integral part a bit before I take the final though.
Differentiation was easy in comparison idk maybe it’ll click when I hear a few different explanations.
Good luck. It's been decades since I've looked at it
It helped me to do it graphically a few times. Use geometry to find the area under a curve.
100%
Do this
Agreed. Integration is the area under the curve the d/dx function makes
Well I get that but I just struggle to integrate things correctly. Especially if involves fractions or trig functions. I can usually make my way through but I’m so slow.
I also still have no idea what dx means and why it just goes away when you integrate
It goes away just because its part of the notation of the function and once you've done the operation that descriptor goes away because you now have juat the result. You get the swirl (operation) with its limits = to something and the dx literally means add the area of all the pieces the function makes within these limits.
Don't feel bad. Some math problems are trivial, like arithmetic or differentiation. And other math problems are fundamentally difficult, like algebra or integration. If you ever meet anyone who disagrees, ask them to solve sin(x)+x=1 for x, or ask them to find the integral of x^x. Believe it or not, these simple problems have no closed form solution. The only way to solve them is to give raw numerical approximations, or to say that the problems are already in their most solved possible form.
Thr best you can do is memorize solutions for small sets of such problems, because there is no generalized strategy.
I also had problems with integration, the Math topic. Never really got it.