![]() And from that, subtract the antiderivativeĮvaluated at 1. ![]() We could evaluate this, by evaluating theĪntiderivative of f, or an antiderivative of f, at 4. Then I can evaluate this thing, and we do a whole video on conceptually X, or another way of saying it is, f, capital F of x is the antiderivative, antiderivative of lower case f of x. ![]() > Which tells us, that if f has anĪntiderivative, so if we have the antiderivative of f, so f of x isĭerivative, derivative of some function capital F of Productive with this, we have to turn to the second fundamental theorem ofĬalculus, sometimes called part two of the fundamental theorem ofĬalculus. The exact area of the un- Between 1 and 4, under the curve f of x,Īnd above the x axis. We've just written some notation that says So that's where the notation of theĭefinite integral comes from. Those infinitely thin rectangles, or the areas of those infinitely thin And so, this part right over here is theĪrea of one of those rectangles, and we were The height of this rectangle is the function evaluated at an x that's within This is how I conceptualize it, is dx, and Infinite number of these rectangles, where the width ofĮach of the rectangles. In fact, that's where the Riemann integralĬomes from. Rectangles, maybe not so infinitely thin. Infinitely thin rectangles that we sum up to find thisĪrea. Imagine a bunch of infinite, an infinite number of The definite integral from 1 to 4 of f ofĬonceptualize where this notation comes from, is we The curve, this little brown shaded area, is And the way we denote the exact area under I wanna find the exact area under thisĬurve above the x axis. This curve and above the positive x axis, between, between x equals 1 and x equalsĤ, x equals 4. The area under the curve, y is equal to f of x, so that's my y axis. So we've got the function, f of x is equal
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