A very important question
The sum of the derivative and integral of a Function equals what?
The sum of the derivative and integral of a function equals the original function itself, plus a constant. This is known as the Fundamental Theorem of Calculus. Mathematically, it can be expressed as:
∫ (f'(x) + f(x)) dx = f(x) + C
where f(x) is the function, f'(x) is its derivative, ∫ is the integral operator, dx represents the differential element, and C is the constant of integration.
The sum of the derivative and integral of a function equals the original function, up to a constant. This statement is known as the Fundamental Theorem of Calculus.
Mathematically, if f(x) is a continuous function on an interval [a, b], then:
∫(a to b) f'(x) dx + ∫(a to b) f(x) dx = f(b) - f(a) + C,
where f'(x) represents the derivative of f(x), ∫ represents the integral, and C is the constant of integration. The Fundamental Theorem of Calculus establishes the connection between derivatives and integrals and highlights that taking the derivative of a function undoes the process of taking its integral.