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Wm_Davies

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In summary, the fundamental theorem of calculus ties together differentiation and integration and makes it easier to solve definite integrals. This theorem can be applied to any function as long as its antiderivative can be found. This makes it a powerful tool in solving a wide range of integration problems.

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Wm_Davies

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quasar987

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And this is where the fundamental theorem of calculus comes into play! It says, well computing the integral of

[tex]

\int_a^bf(x)dx = F(b)-F(a)

[/tex]

Voila!

The Fundamental Theorem of Calculus is a fundamental concept in calculus that establishes a connection between the two major branches of calculus: differential calculus and integral calculus. It states that differentiation and integration are inverse operations, meaning that the derivative of a function is equal to the original function when integrated.

The Fundamental Theorem of Calculus is significant because it allows for the evaluation of definite integrals without having to use Riemann sums or other complicated methods. It also provides a way to easily find the antiderivative of a function, which is important in many areas of mathematics and science.

To use the Fundamental Theorem of Calculus, you first need to find the antiderivative of the function you are integrating. Then, you can simply substitute the upper and lower limits of integration into the antiderivative and subtract the two values to find the definite integral.

The first part of the Fundamental Theorem of Calculus states that if a function is continuous on a closed interval, then the definite integral of that function can be evaluated by finding its antiderivative and evaluating it at the upper and lower limits of integration. The second part of the theorem states that if a function is continuous on a closed interval, then the derivative of the definite integral of that function is equal to the original function.

No, the Fundamental Theorem of Calculus can only be applied to certain types of functions, specifically those that are continuous on a closed interval. This means that the function must not have any "jumps" or discontinuities within the interval. Additionally, the function must have a well-defined antiderivative, which is not always the case for all functions.

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