>>11422764you can learn them from this post right here yes yes yes yes ok so to find the integral of x^2 you get a square based pyramid with height x and area of base x^2, if you find the volume you get 1/3x^3, why is this an integral? ok ok don't you agree that an integral is in some way the sum of the y values of a graph from x = 0 to x = the integral's x value with the y values being multiplied by infinitesimals? OK now think, the square base of this square base pyramid, it got side length x and it makes area x^2, now, THIS IS THE REALLY EXCITING BIT, AS YOU MOVE UP THE SQUARE BASED PYRAMID, WHAT HAPPENS TO THE AREA OF THE SQUARE BASE?? IT DECREASES AT A RATE OF 2X!!! THE DERIVATIVE OF THE AREA OF THE SQUARE BASE!!! THE HEIGHT OF THE PYRAMID IS THE X VALUE OF THE INTEGRAL, SUMMING ALL OF THE X^2s FROM 0 TO X, IT IS THE SUM OF THE EVER INCREASING SQUARE SLICE OF THE SQUARE BASED PYRAMID AS IT MOVES DOWN THE PYRAMID!!! SUCH JOY!!
