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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.
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Which is harder differential calculus or integral calculus?
Im still taking Integral Calculus now, but for me, if you dont know Differential Calculus you will not know Integral Calculus, because Integral Calculus need Differential. So, as an answer to that question, ITS FAIR
Difference between integral and differential calculus?
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
What is another term for Calculus?
Analysis is a broader term for Calculus and the theorems behind it. It is studied both with real and complex numbers as real and complex analysis. Usually calculus just deals with the basic problems of differential calculus and integral calculus.
What course to take before advanced calculus?
You must have a strong basis in Algebra, Algebra II, Geometry and Trigonometry. Usually high schools offer a pre-Calculus course which is somewhat of a conglomeration of the aforementioned courses. Then you would move into differential calculus, integral calculus, vector (multi-variable) calculus, and finally differential equations, which is considered to be at the top of the hierarchy of the calculus courses. So take Algebra, Algebra II, Geometry and Trigonometry to get your strong foundation before begining the calculus sequence.
Who is the father of integral calculus?
Liebniz and Newton
