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holy shit, this genuinely feels so obvious now that you explained how it works, but this is literally never clicked for me. I am the definition of mnd blown rn.
6:02 , the indefinite integral should have had abs value around f(x), bc f(x)=x+1 has negative f(x) values. I.e. ln|(x+1)| + C, where x ≠-1 Original function had domain (-inf,-1)U(-1,+inf) You get an anti derivative at every point defined in the original domain.
Anything times the rate of decay, equals everything adds up to what it adds up to until it decays and isn't what it once was. Even the universe expanding times the rate of decay, means the universe isn't expanding much more then it decays. What would be a good way to explain the rate of decay in a mathematical formulation.
i have one question, if f(x) and g(x) are parametric equations to each other, when thinking about the graph formed, the integrals you are calculating wont really be the integrals of the functions themselves, but rather some representation of them to fit into the parametric equation. Can someone explain why this works?
thank you for your video !!! But i have a question at 3:10 you rotate the x and y axis to calculate the area between y1 and y2 but what if instead of an exponential curve as here , we had a cos function then the cos function would be (rotated too ) and what sense would calculating the area under this curve have ?
analytic continuation is a concept similar to piecewise functions, or i should say, it's not defined as the sum of the reciprocal of all the natural numbers raised to the input power anymore.
