First Fundamental Theorem of Calculus 2

Visualizing the Definite Integral on the Graphs of the Integrand and Its Antiderivative
In the App[br] Enter the formula for the integrand function [i]f[/i] in its input box in the left window[br] Enter choices for the limits of integration [i]a[/i] and [i]b[/i] via the sliders or input boxes.[br] [br]In the Left Window[br] You will see the graph of the integrand function f(x) graphed in red.[br] You will see the definite integral expressed as a net signed area between the graph of [i]f[/i]([i]x[/i]) and the [i]x[/i]-axis. [br] The integral is equal to the green shaded area minus the red shaded area.[br] The notation for the integral and its approximate value are displayed.[br][br]In the Right Window[br] You will see the formula for an antiderivative function [i]F[/i]([i]x[/i]). [br] This is the antiderivative function generated by GeoGebra plus the constant [i]C[/i].[br] Adjust the value of C via the slider or input box to obtain another antiderivative function.[br] The graph of [i]F[/i]([i]x[/i]) is in blue.[br] F is an antiderivative of f and f is the derivative of [i]F[/i]: [i]F[/i] ' ([i]x[/i]) = [i]f[/i]([i]x[/i]).[br] You will see the values of F(b) and F(a) and the value of [i]F[/i]([i]b[/i]) - [i]F[/i]([i]a[/i]) in the box and illustrated on the graph.[br] The integral is equal to [i]F[/i]([i]b[/i]) - [i]F[/i]([i]a[/i]).[br] You will see the integral illustrated as the signed length ([i]F[/i]([i]b[/i]) - [i]F[/i]([i]a[/i])) of the illustrated vertical vector.[br] The First Fundamental Theorem of Calculus as it applies to definite integrals is stated.

Information: First Fundamental Theorem of Calculus 2