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4 days ago · Fundamental theorem of calculus, Basic principle of calculus. It relates the derivative to the integral and provides the principal method for evaluating definite integrals (see differential calculus; integral calculus). In brief, it states that any function that is continuous (see continuity) over.
- The Editors of Encyclopaedia Britannica
As you may recall from the Fundamental Theorem of Calculus, the integral is the inverse operation to differentiation: \[\int \dfrac{d f}{d x} d x=f(x)+C \nonumber \] It is not always easy to evaluate a given integral. In fact some integrals are not even doable! However, you learned in calculus that there are some methods that could yield an answer.
6 days ago · In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.
4 days ago · Differentiation is a basic mathematical concept that deals with the rate at which a function changes. Moreover, it is a mathematical process used to find the derivative of a function. This represents the tangent line’s slope to the function’s graph at any point.
5 days ago · Define and use vector operations in two and three dimensions. Demonstrate an understanding of partial derivatives and multiple integrals. Perform applications of partial derivatives and multiple integrals. Understand the fundamentals of vector space calculus including the Green, Gauss and Stokes theorems.
3 days ago · I derive the formula for the arc length formula for a smooth curve. I use the mean value theorem using the fact that arc length curve has to be continuously ...
- 19 min
- Virgilio Cerna Choto
4 days ago · Differential calculus arose from trying to solve the problem of determining the slope of a line tangent to a curve at a point. The slope of the tangent line indicates the instantaneous rate of change of the function.
