Evaluate the following definite integral
$integral subscript 0 superscript straight pi over 4 end superscript space sin space 2 straight x space dx$

Solution

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

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Integrals

Evaluate the following definite integral
$integral subscript 0 superscript straight pi over 4 end superscript space sin space 2 straight x space dx$

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