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Evaluate the integral. integral_0^{pi / 4} sin^4 (4 x) dx

Question:

Evaluate the integral.

{eq}\displaystyle \int_0^{\dfrac \pi 4} \sin^4 (4 x)\ dx {/eq}

Integration using Trigonometric Identity

Here, to solve the integral, we are using the trigonometric identity. Here, we are using {eq}\displaystyle \cos (2\theta) = 2\cos^2 \theta -1 {/eq} and then after integrating we will find the required value.

Answer and Explanation: 1

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Let {eq}I = \displaystyle \int_0^{\dfrac \pi 4} \sin^4 (4 x)\ dx {/eq}

Using the property

{eq}\displaystyle \cos (2\theta) = 2\cos^2 \theta...

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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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