वक्र y = sin x, y = cos x, 0 ≤ x ≤ π/2 के बीच संलग्न क्षेत्र क्या है?

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Question

This question was previously asked in

UP TGT Mathematics 2019 Official Paper

Answer 1

गणना:

F1 Tapesh 25.2.21 Pallavi D 3

संलग्न क्षेत्र

\( = 2\mathop \smallint \nolimits_0^{\pi /4} \left( {\cos x - \sin x} \right)dx\)

\( = 2\left[ {\sin x + \cos x} \right]_0^{\pi /4}\)

\( = 2\left[ {\left( {\frac{1}{{\sqrt 2 }} + \frac{1}{{\sqrt 2 }}} \right) - \left( {0 + 1} \right)} \right]\)

\( = 2\left( {\sqrt 2 - 1} \right)\)