Evaluate the following definite integral
$integral subscript 0 superscript straight pi open parentheses sin squared straight x over 2 minus cos squared straight x over 2 close parentheses space dx$

Solution

Let I = $integral subscript 0 superscript straight pi open parentheses sin squared straight x over 2 minus cos squared straight x over 2 close parentheses dx$
$equals negative integral subscript 0 superscript straight pi open parentheses cos squared straight x over 2 minus sin squared straight x over 2 close parentheses dx space equals space minus integral subscript 0 superscript straight pi cosx space dx space equals space minus open square brackets sin space straight x close square brackets subscript 0 superscript straight pi equals negative left parenthesis sin space straight pi space minus space sin space 0 right parenthesis space equals space minus left parenthesis 0 minus 0 right parenthesis space equals space 0$

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Integrals

Evaluate the following definite integral
$integral subscript 0 superscript straight pi open parentheses sin squared straight x over 2 minus cos squared straight x over 2 close parentheses space dx$

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