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What is the relationship of integral and differential calculus?
We say function F is an anti derivative, or indefinite integral of f if F' = f. Also, if f has an anti-derivative and is integrable on interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a) Thirdly, Let F(x) be the definite integral of integrable function f from a to x for all x in [a, b] of f, then F is an anti-derivative of f on [a,b] The definition of indefinite integral as anti-derivative, and the relation of definite integral with anti-derivative, we can conclude that integration and differentiation can be considered as two opposite operations.
How does calculus help us?
It is used in physics all the time. For example, acceleration is the derivative of velocity which is a derivative of position with respect to time. Calculating the amount of work done in a vector field (like an electrical field) also uses calculus.
Scientist who made calculus?
Newton is the named founder of Calculus. Yet there is controversy because it is claimed that Leibniz stole Newton's Calculus notes and took all credit for Calculus. But to this day Leibniz's integral and derivative notation is more commonly used that Newton's which was found confusing.
What is the fundamental theory of calculus?
The fundamental theorum of calculus states that a definite integral from a to b is equivalent to the antiderivative's expression of b minus the antiderivative expression of a.
Why was the calculus student confused about y equals ex and the derivative of y equals ex?
Because the derivative of e^x is e^x (the original function back again). This is the only function that has this behavior.
