What is an antiderivative of a function?

An antiderivative of a function f(x) is a function whose derivative is equal to f(x). It is not one function but a family of functions, differing by constants; and so the answer must have a ‘+ constant’ term to indicate all antiderivatives. A definite integral, on the other hand, is an integral with terminals.

What is an antiderivative of a function f give an example?

Example: F(x)=x3 is an antiderivative of f(x)=3×2. Also, x3+7 is an anti-derivative of 3×2, since d(x3)dx=3×2 and d(x3+7)dx=3×2. The most general antiderivative of f is F(x)=x3+C, where c is an arbitrary constant.

Is the antiderivative the same as the integral?

Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

What are the applications of derivatives?

Applications of Derivatives in Maths

• Finding Rate of Change of a Quantity.
• Finding the Approximation Value.
• Finding the equation of a Tangent and Normal To a Curve.
• Finding Maxima and Minima, and Point of Inflection.
• Determining Increasing and Decreasing Functions.

How integration is antiderivative?

Indefinite integral means integrating a function without any limit but in definite integral there are upper and lower limits, in the other words we called that the interval of integration. The antiderivative of x² is F(x) = ⅓ x³. The definite integral, however, is ∫ x² dx from a to b = F(b) – F(a) = ⅓ (b³ – a³).

How to find the antiderivative?

xndx = xn+1+c as long as n does not equal -1. This is essentially the power rule for derivatives in reverse

What is anti derivative in calculus?

An anti-derivative is basically an integral, which is the second main concept of calculus. When doing a derivative you take away a power, when doing an anti-derivative, you add a power, in otherwords it undoes whatever a derivative does.

What is the antiderivative of sec(x)?

The antiderivative of sec(x) is equal to ln |sec(x) + tan(x)| + C, where C represents a constant. This antiderivative, also known as an integral, can be solved by using the integration technique known as substitution.

Is an integral an antiderivative?

In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F ′ = f {\\displaystyle F’=f} .