Evaluate {eq}\displaystyle \int\frac{\displaystyle y}{\displaystyle \sqrt{16-9y^4}} dy {/eq}.

Question:

Evaluate {eq}\displaystyle \int\frac{\displaystyle y}{\displaystyle \sqrt{16-9y^4}} dy {/eq}.

Substitution rule:

In integration substitution rule is used to calculate integration of the given problem. Any difficult problem we can't integrate directly. In such types of situation, we have taken some function as u and then find the integration.

Answer and Explanation: 1

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Given that {eq}\displaystyle \int\frac{\displaystyle y}{\displaystyle \sqrt{16-9y^4}} dy {/eq}.

Apply u-substitution {eq}\:u=y^2, du=2ydy {/eq}

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Substitution Techniques for Difficult Integrals

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Chapter 13 / Lesson 6
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Some integrals, such as those exploring cyclical functions, cannot be solved with basic math tools. Learn how to use tabular and ~'u~' substitution techniques to solve difficult integrals.


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