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Use Antiderivatives and Definite Integrals Theorem to evaluate the integral.

{eq}\int^2_0 4x^3 dx {/eq}

Question:

Use Antiderivatives and Definite Integrals Theorem to evaluate the integral.

{eq}\int^2_0 4x^3 dx {/eq}

Fundamental Theorem of Calculus

Evaluating a definite integral is most easily done by applying the Fundamental Theorem of Calculus. If we can find an antiderivative for the integrand, then the formula that will lead us to the result of this integral.

{eq}\int_a^b f(x) dx = F(b) - F(a) {/eq}

Answer and Explanation: 1

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The function that we are aiming to integrate is a monomial, and the antiderivative of a monomial can be found by reversing the power rule. This allows...

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Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.


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