By using the properties of definite integrals, evaluate the following integral.
$integral subscript 0 superscript straight pi over 2 end superscript space cos squared space dx$

Solution

Let I = $integral subscript 0 superscript straight pi over 2 end superscript cos squared xdx space equals space 1 half integral subscript 0 superscript straight pi over 2 end superscript left parenthesis 1 plus cos 2 straight x right parenthesis space dx space equals space 1 half open square brackets straight x plus fraction numerator sin 2 straight x over denominator 2 end fraction close square brackets subscript 0 superscript straight pi over 2 end superscript$
$equals space 1 half open square brackets open parentheses straight pi over 2 plus 1 half sin space straight pi close parentheses minus open parentheses 0 plus fraction numerator 1 over denominator 2 space end fraction sin 0 close parentheses close square brackets space equals space 1 half open square brackets straight pi over 2 plus 1 half left parenthesis 0 right parenthesis minus 0 minus 0 close square brackets space equals space straight pi over 4$

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Integrals

By using the properties of definite integrals, evaluate the following integral.
$integral subscript 0 superscript straight pi over 2 end superscript space cos squared space dx$

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