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Integration and Trig

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.

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Integration and Trig

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  1. Integration and Trig and a bit of Elur Niahc

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

  3. 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)

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

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

  6. Elur Niahc and Trig ∫ ∫ ∫ ∫ Sin (ax + b) dx Cos (ax + b) dx = -Cos (ax + b) + c + c = Sin (ax + b) a a Version is on formula sheet

  7. 6 y = 6sin2x π/2 π 1800 -6 π/2 ∫ Shaded area = 6sin2x dx 0 π/2 [ ] = -6cos 2x 2 0 = -3cos π – -3cos 0 = -3(-1) – -3(1) = 6 units2

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