Find the indefinite integral using the substitution x = 4 sin theta. integral fraction square...

Question:

Find the indefinite integral using the substitution {eq}\rm x = 4 \sin \theta. {/eq}

{eq}\rm \displaystyle \int \dfrac{ \sqrt {16 - x^2}}{x^2}dx {/eq}

Indefinite Integral:

Substitution method to solve indefinite integral is applied as when {eq}\int{f\left( x \right)dx}{/eq} is given. Consider {eq}x=g\left( t \right){/eq} then differentiate both sides with respect to {eq}t{/eq} and find the value of {eq}dx{/eq} hence using the value of {eq}x{/eq} and {eq}dx{/eq} in terms of {eq}t{/eq} simplifying the integral we get the value of the integral.

Answer and Explanation: 1

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Given:

• The given integral is {eq}\int{\frac{\sqrt{16-{{x}^{2}}}}{{{x}^{2}}}dx}{/eq} and {eq}x=4\sin \theta {/eq}.

To find...

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