Use the trigonometric substitution x = 2 sin theta to find the integral integral_0^1 1 / {square...


Use the trigonometric substitution {eq}x = 2 \sin \theta {/eq} to find the integral {eq}\displaystyle \int_0^1 \dfrac 1 {\sqrt {4 - x^2}}\ dx {/eq}.

Integration by Substitution:

In calculus, Integration by substitution is a technique to solve the complicated integral by transforming the integral into a simple integral. In this technique, we replace the integrand variable with another variable such as the trigonometric variable.

Answer and Explanation: 1

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Given Data

  • The given definite integral is {eq}\displaystyle \int\limits_0^1 {\dfrac{1}{{\sqrt {4 - {x^2}} }}} dx {/eq}.

Using the integration by...

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Learn more about this topic:

Understanding Trigonometric Substitution


Chapter 13 / Lesson 11

What is trig substitution for integrals? See examples to understand integration by trigonometric substitution using the three trig substitution identities.

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