The area bounded by the x-axis, y = cosx and y = sin x when $0 less or equal than straight x less or equal than straight pi over 2$

$2 left parenthesis square root of 2 minus 1 right parenthesis$
$square root of 2 minus 1$
$square root of 2 plus 1$
$square root of 2$

Solution

square root of 2 minus 1

The two curves y = sin x and y = cos x meet where sin x = cos x , i.e., where x = 1
$rightwards double arrow space space space space straight x space equals space straight pi over 4.$
Required area (show shaded)
$equals space integral subscript 0 superscript straight pi over 4 end superscript left parenthesis cosx space minus space sinx right parenthesis space dx equals space open square brackets sinx space plus space cosx close square brackets subscript 0 superscript straight pi over 4 end superscript space equals space sin space straight pi over 4 plus cos space straight pi over 4 minus left parenthesis 0 plus 1 right parenthesis equals space fraction numerator 1 over denominator square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 end fraction minus 1 space equals space fraction numerator 2 over denominator square root of 2 end fraction minus 1 space equals space square root of 2 minus 1.$

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Vector Algebra

The area bounded by the x-axis, y = cosx and y = sin x when $0 less or equal than straight x less or equal than straight pi over 2$

$2 left parenthesis square root of 2 minus 1 right parenthesis$
$square root of 2 minus 1$
$square root of 2 plus 1$
$square root of 2$

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