Integration and Trig and a bit of Elur Niahc.

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Presentation transcript:

Integration and Trig and a bit of Elur Niahc

What is to be learned? How to integrate trig functions How to apply Elur Niahc to trig functions

Fast Track y = sin(3x + 10) , where U = 3x + 10 let y = sin U dy/du du/dx = 3 = cos U ÷ 3 = Cos U dy/dx 3 = 3Cos(3x + 10)

∫ ∫ ∫ Cos (ax + b) dx = Sin (ax + b) a Cos (2x + 7) dx = Sin(2x + 7)

∫ ∫ Sin (ax + b) dx = -Cos (ax + b) a ∫ Sin 4x dx = -Cos 4x + c 4

∫ ∫ ∫ ∫ Elur Niahc and Trig Sin (ax + b) dx Cos (ax + b) dx Version is on formula sheet

∫ [ ] 6 y = 6sin2x π/2 π 1800 -6 π/2 Shaded area = 6sin2x dx π/2 π/2 [ ] = -6cos 2x 2 = -3cos π – -3cos 0 = -3(-1) – -3(1) = 6 units2