# Keyword Analysis & Research: fundamental theorem of calculus area

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What does the fundamental theorem of calculus Part 1 state?

Answer: The fundamental theorem of calculus part 1 states that the derivative of the integral of a function gives the integrand; that is distinction and integration are inverse operations. In addition, they cancel each other out. Moreover, the integral function is an anti-derivative.

What is the anti-derivative in the fundamental theorem of calculus?

Answer: As per the fundamental theorem of calculus part 2 states that it holds for ∫a continuous function on an open interval Ι and a any point in I. Furthermore, it states that if F is defined by the integral (anti-derivative). Question 6: Are anti-derivatives and integrals the same?

How to solve i 1 in calculus Part 1?

To solve I 1, we will use the rule of integration by parts. According to this rule, Let, The first function = f (x) = x and the second function = g (x) = e x. Therefore, Question 4: State the fundamental theorem of calculus part 1?

What is the mean value theorem for integrals?

Before we get to this crucial theorem, however, let’s examine another important theorem, the Mean Value Theorem for Integrals, which is needed to prove the Fundamental Theorem of Calculus. The Mean Value Theorem for Integrals states that a continuous function on a closed interval takes on its average value at the same point in that interval.