Integration and the Logarithmic Function

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Presentation transcript:

Integration and the Logarithmic Function dx x 1 x ∫ dx = ∫ = logex + C f’(x) f(x) ∫ = dx logef(x) + C Exercise 4.6 (page 146)

Integration and the Logarithmic Function Example 1/3 [ ] logex 1 2 2 1 x ∫ Area = dx = 1 = loge2 – loge1 = loge(2÷1) Exercise 4.6 (page 146) = loge2 units2

Integration and the Logarithmic Function f’(x) f(x) = dy dx Example 2/3 x2 x3 + 7 3x2 x3 + 7 ∫ dx 1 3 ∫ dx = = loge(x3 + 7) + C 1 3 Exercise 4.6 (page 146) f’(x) f(x) ∫ = dx logef(x) + C

Integration and the Logarithmic Function f’(x) f(x) = dy dx Example 3/3 x + 1 x2 + 2x + 4 2(x + 1) x2 + 2x + 4 ∫ dx 1 2 ∫ dx = 2x + 2 x2 + 2x + 4 ∫ dx 1 2 = Exercise 4.6 (page 146) = loge(x2 + 2x + 4) + C 1 2