Evaluate the integral.
{eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \sin^2 x \cos^2 x dx {/eq}
Question:
Evaluate the integral.
{eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \sin^2 x \cos^2 x dx {/eq}
Trigonometric Identities in Integrals:
One of the ways of evaluating integrals involving trigonometric functions is by implementing trigonometric identities.
Some of the trigonometric identities we can implement are:
{eq}2\sin(x) \cos(x) = \sin(2x) {/eq}
{eq}\sin^2(x) = \displaystyle \frac{1-\cos(2x)}{2} {/eq}
Answer and Explanation:
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View this answerFirst, we have to rewrite the integral by applying {eq}2\sin(x) \cos(x) = \sin(2x) {/eq} and {eq}\sin^2(x) = \displaystyle...
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Chapter 23 / Lesson 1Learn to define basic trigonometric identities. Discover the double-angle, half-angle, and other identities. Learn how to use trigonometric identities. See examples.