Calculus Assignment
What is the Fundamental Theorem of Calculus?
The Fundamental Theorem of Calculus is a mathematical theorem that relates the two branches of calculus: integral and differential calculus. The link between these two areas is established by the fact that differentiation can be used to compute definite integrals and integration can be used to find antiderivatives.
In words, it states that if functions F(x) and f(x) are related as follows :
F’ (x)=f (x), then we have ∫abF(x)dx=F(b)-F(a).
In summary, the fundamental theorem of calculus links together both differential and integral calculations in order to solve problems more quicklyized model based on past data sets. The Fundamental Theorem of Calculus states that the integration and differentiation operations in calculus are inverse to each other. This means that one can move from a definite integral (the area under a curve) to its corresponding derivative, or vice versa.
In practice, this theorem allows for easier calculation when trying to solve complex problems involving derivatives and integrals by breaking them down into simpler pieces.
At the end of the day, understanding how these two parts tie together is essential in correctly applying both methods throughout all branches of mathematical sciences.
