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


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

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Indefinite Integrals as Anti Derivatives


Chapter 12 / Lesson 11

Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.

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