Evaluate the definite integral. Hint: Use partial fractions. integral 2^3 fraction 5x + 1 2x^2 -...


Evaluate the definite integral.

Hint: Use partial fractions.

{eq}\displaystyle \int_2^3 \dfrac{5x + 1}{2x^2 - x - 1} \ dx {/eq}

Evaluating a Definite Integral:

To solve a definite integral, we must use the Fundamental Theorem of Calculus, i.e.,

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

The result of a definite integral can be zero, a positive number, or a negative number.

Answer and Explanation: 1

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Let's evaluate the definite integral.

{eq}\displaystyle \int_2^3 \dfrac{5x + 1}{2x^2 - x - 1} \ dx {/eq}

Factoring the denominator, we have


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Evaluating Definite Integrals Using the Fundamental Theorem


Chapter 16 / Lesson 2

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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