Integrating sinx & cosx

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Example∫π/ 3/0 3sinx dx = [-3cosx ]30π= (-3cos π / 3) - (-3cos0)Example= (-3 X ½ ) – (-3 X 1)= -1 1 / 2+ 3= 1 1 / 2Find the totalshaded area.π3π/ 2y = sinx

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π1 st area = ∫ sinx dx0= [ -cosx ] 0π= -cosπ - (- cos0)= -(-1) – ( -1)= 23π/ 22nd area = ∫ sinx dxπ= [ -cosx ]π3π/ 2= -cos 3 π / 2- (- cos π)= 0 - 1= -1 (actual area = 1)So total area = 2 + 1 = 3units 2alternativelyBy symmetry,2 nd area = ½ of first = 1 etc.

Page 1: Integrating sinx & cosxIf y = sinx
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Integrating sinx & cosx

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