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Evaluate the integral \int \frac{x}{\sqrt{9-4x^2}} \,dx

Question:

Evaluate the integral {eq}\int \frac{x}{\sqrt{9-4x^2}} \,dx {/eq}

Integral:

The problem can be solved by using the substitution where we will put {eq}9-4x^{2}=t {/eq} and then differentiate it to get the value of dx and then put it in the integral and then integrate using the exponential rule.

Answer and Explanation: 1

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To solve the integral we will proceed as

{eq}\int \frac{xdx}{\sqrt{9-4x^{2}}}dx {/eq}

Now we will use the substitution method

Put

{eq}9-4x^{2}=t\...

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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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