Integrating sinx & cosx

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Example Show that the shaded area = 2√2units 2 .y = cosxy = sinxLimits Curves meet when sinx = cosxsinx = cosxcosx cosxtanx = 1x = π / 4or 5 π / 4Q1 & Q3tan -1 1 = π / 4

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Between π/ 4and 5 π / 4the sin graph is higherSo shaded area = ∫ π/ 45π/ 4( sinx – cosx )dx= [ -cosx - sinx ]5π/ 4π/ 4= ( -cos 5 π / 4- sin 5 π / 4) - (-cos π / 4- sin π / 4)= ( 1 / √2+ 1 / √2 ) - (- 1 / √2- 1 / √2 )= 1 / √2+ 1 / √2+ 1 / √2+ 1 / √2= 4 / √2= 4 X √2√2 X √2= 4√22= 2√2units 2

Page 1 and 2: Integrating sinx & cosxIf y = sinx
Page 3: π1 st area = ∫ sinx dx0= [ -cosx

Integrating sinx & cosx

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