Evaluate {eq}\displaystyle \int_{0}^{\frac{\pi }{4}}\sin ^{2}(2x)\cos ^{2}(2x) \ dx {/eq}
Question:
Evaluate {eq}\displaystyle \int_{0}^{\frac{\pi }{4}}\sin ^{2}(2x)\cos ^{2}(2x) \ dx {/eq}
Using Trignometric Identities to Evaluate Integrals:
When we have an integral that contains a trig expression, we can often simplify the trig expression by applying trig identities. Two trig identities that are useful in this problem in particular are
{eq}\sin 2\theta ={2} \sin \theta \cos \theta {/eq}
and
{eq}\sin^2 \theta = \frac{1}{2} \left[ 1-\cos 2\theta \right] {/eq}
Answer and Explanation: 1
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View this answerFirst, we simplify the integral using the following formula:
{eq}\sin 2\theta = {2} \sin \theta \cos \theta\\ \sin 4x= {2} \sin 2x \cos 2x...
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Chapter 12 / Lesson 2Understand that an integral measures the area under a curve, and learn how to evaluate linear and polynomial integrals. Explore different applications of integrals with examples.