In this video two important integrals of sine squared and cosine squared are calculated using trigonometric identities instead of integration by parts. The double angle identity is applied to simplify the integrals, which can be split into manageable fractions. The solutions involve integrating basic functions, resulting in expressions involving x and trigonometric functions. The same technique is used for both integrals, with only a sign difference between them. The video aims to provide an alternative method for solving these common integrals, saving time and effort when encountered in exercises.
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