6 2 Notes
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Integration by parts is a technique for integrating functions that are products. It involves setting one factor as u and the other as dv, where u is chosen to be the factor with the simpler derivative and dv is chosen to have an integral that fits a basic integration formula. Common uses involve integrating powers of x multiplied by exponential or trigonometric functions.
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6 2 Notes
- 1. 6.2 Integration By Parts Goal: to integrate functions that are productsProduct RuleLet f(x) and g(x) be a differentiable functions of x
- 3. We need to figure out: which factor is the easier factor to take the derivative of (u or f(x)) and which one is easier to integrate (dv or g’(x))Guidelines:Let u have a derivative simpler than itself (like a general power rule derivative)
- 4. Let dv be the most complex function that fits a basic integration formula (like ex)Most common uses of integration by parts:
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- 6. 2 Most common uses of integration by parts:
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- 8. 4Examples: