Question

By using the properties of definite integrals, evaluate
$integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript cosx space dx$

Solution

Let
$straight I space equals space integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript cosx space dx space equals space 2 integral subscript 0 superscript straight pi over 2 end superscript space cosx space dx$
[∴ cos x is an even function as cos (–x) = cos x]
$equals space 2 open square brackets sin space straight x close square brackets subscript 0 superscript straight pi divided by 2 end superscript space equals space 2 open parentheses sin straight pi over 2 minus sin space 0 close parentheses space equals space 2 space left parenthesis 1 minus 0 right parenthesis space equals space 2.$

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Integrals

By using the properties of definite integrals, evaluate
$integral subscript negative straight pi over 2 end subscript superscript straight pi over 2 end superscript cosx space dx$

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