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Integration 2

Integration 2. What is to be learned?. How to integrate composite functions. Fast Tracking. y = (7x + 2) 5. let y= u 5. where u = 7x + 2. dy / du. = 5u 4. du / dx. = 7. dy / dx. =. dy / du. du / dx. = 5u 4. 7. dy / dx. Add 1 to power. =5(7x + 2) 4. 7. Fast Tracking.

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Integration 2

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  1. Integration 2

  2. What is to be learned? • How to integrate composite functions

  3. Fast Tracking y = (7x + 2)5 let y= u5 where u = 7x + 2 dy/du = 5u4 du/dx = 7 dy/dx = dy/du du/dx = 5u4 7 dy/dx Add 1 to power =5(7x + 2)4 7

  4. Fast Tracking y = (7x + 2)5 let y= u5 where u = 7x + 2 dy/du = 5u4 du/dx = 7 dy/dx = dy/du du/dx ÷ 5 = 5u4 7 dy/dx Add 1 to power =5(7x + 2)4 7

  5. Fast Tracking y = (7x + 2)5 let y= u5 where u = 7x + 2 dy/du = 5u4 du/dx = 7 ÷ 7 dy/dx = dy/du du/dx ÷ 5 = 5u4 7 dy/dx Add 1 to power =5(7x + 2)4 7

  6. ∫ ∫ (ax + b)n (ax + b)n dx Elur Niahc = (ax + b)n+1 a (n+1) ∫ (5x + 7)3 dx = (5x + 7)4 (4) 5 = (5x + 7)4 + c 20

  7. ∫ (9x + 3)6 dx = (9x + 3)7 9 (7) = (9x + 3)7 + c 63 ∫ 9(5 – 4x)7 dx = 9(5 – 4x)8 (8) -4 = 9(5 – 4x)8 + c -32

  8. Integration 2 Elur Niahc ∫ ∫ (ax + b)n (ax + b)n dx = (ax + b)n+1 + c a (n+1) ∫ (3x + 8)6 dx = (3x + 8)7 (7) 3 = (3x + 8)7 + c 21

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