Horizontal integration is where the slices are parallel to the x-axis, instead of to the y-axis. In this case, you would be integrating f(y)dy, instead of f(x)dx.
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right is defined as the positive direction
it's Q Bar. i cant find a symbol for it on the keyboard. but its basically like The rational Symbol (Q) with a horzontal line on top of it.
Integration by Parts is a special method of integration that is often useful when two functions.
Assuming integration is with respect to a variable, x, the answer is 34x + c where c is the constant of integration.