(a) integrate to find F as a function of x and (b) demonstrate the Second Fundamental Theorem of

step 1 In this question you have f of x is equal to 4 to x integration of root t d t so this is equal t

(a) integrate to find F as a function of x and (b)...

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Key Concepts

Antiderivative

An antiderivative of a function represents another function whose derivative is the original function. In the context of integration, finding the antiderivative is equivalent to reversing the process of differentiation. When evaluating a definite integral, the antiderivative is calculated at the boundaries and the difference gives the net accumulated value between those points.

Definite Integral

A definite integral computes the net area under the curve of a function between specified limits. It can be interpreted as the accumulated quantity or total accumulation of the function over an interval. The computation uses the antiderivative, evaluating it at the upper and lower limits and taking their difference, as established by the Fundamental Theorem of Calculus.

Second Fundamental Theorem of Calculus

The Second Fundamental Theorem of Calculus states that if a function is continuous over an interval, then the derivative of the definite integral of that function with a variable upper limit is the original function evaluated at that limit. This theorem establishes a direct link between integration and differentiation, showing that integration can be ‘undone’ by differentiation.

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