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Evaluate integral^{fraction {1}{5} }_{ - fraction {1}{5} }e^{5x} dx.

Question:

Evaluate {eq}\displaystyle \int^{\frac {1}{5} }_{ - \frac {1}{5} }e^{5x} \ dx. {/eq}

Definite Integral in Calculus:

The definite integral is used to compute the exact area. We are given an exponential function and we need to find out the definite integral.

To solve this problem, we'll use the common integral: {eq}\displaystyle \int e^{ax} \ dx = \dfrac{e^{ax}}{a}+C {/eq}.

Next, Plug in the bounds and simplify the answer.

Answer and Explanation: 1

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We are given:

{eq}\displaystyle \int^{\frac {1}{5} }_{ - \frac {1}{5} }e^{5x} \ dx {/eq}

Apply the common integral {eq}\displaystyle \int e^{5x} \...

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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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