What is the geometrical interpretation of an indefinite integral?

∫f(x)dx=F(x)+C represents a family of curves and different values of C corresponds to different members of this family. These members can be obtained by shifting any one of the curves parallel to itself. Above statement can be considered as geometrical representation of indefinite integral.

What is geometric representation of integrals?

In mathematics, integral geometry is the theory of measures on a geometrical space invariant under the symmetry group of that space. Such transformations often take the form of integral transforms such as the Radon transform and its generalizations.

What is geometrical interpretation?

Instead, to “interpret geometrically” simply means to take something that is not originally/inherently within the realm of geometry and represent it visually with something other than equations or just numbers (e.g., tables).

What is the difference between definite & indefinite integrals explain the geometrical interpretations of these?

The definite integral is different from the indefinite integral as follows: Indefinite integral lays the base for definite integral. Indefinite integral defines the calculation of indefinite area whereas definite integral is finding area with specified limits.

Which is the same as Antidifferentiation?

Anti-differentiation or integration is the reverse process to differentiation. For example, if f (x) = 2x, we know that this is the derivative of f(x) = x2.

What is the geometric interpretation of the dot product?

Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates.

What is geometric interpretation of derivative?

Geometrically, the derivative of a function at a given point is the slope of the tangent to at the point . Obviously, this angle will be related to the slope of the straight line, which we have said to be the value of the derivative at the given point. …

What is definite and indefinite integration?

A definite integral has upper and lower limits on the integrals, and it’s called definite because, at the end of the problem, we have a number – it is a definite answer. Indefinite integral is more of a general form of integration, and it can be interpreted as the anti-derivative of the considered function.

What is geometric interpolation?

Geometric interpolation schemes are an important tool for approximation of curves. The basic idea: parameter values are not prescribed in advance. The freedom of choosing a parametrization is used to increase an approximation order and to improve the shape of the interpolant.