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CHAPTER 2 2.4 Continuity Integration by Parts The formula for integration by parts f (x) g’(x) dx = f (x) g(x) - g(x) f’(x) dx. Substitution Rule that is easy to remember Let u = f (x) and v = g(x). Then the differentials are du = f’(x) dx and dv = g’(x) dx and the formula is: u dv = u v - v du.
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Example: Find x cos x dx. Example: Evaluate t 2 e t dt. a b f (x) g’(x) dx = [f (x) g(x)] a b - a b g(x) f ’(x) dx. Example: Evaluate 0 1 tan - 1 x dx. Example: Evaluate x ln x dx. Example: Evaluate (2x + 3) e x dx.
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a b f (x) g’(x) dx = [f (x) g(x)] a b - a b g(x) f ’(x) dx. Example: Evaluate 0 1 tan - 1 x dx. Example: Evaluate 1 e x ln x dx. Example: Evaluate 0 1 (2x + 3) e x dx.
![ a b f (x) g’(x) dx = [f (x) g(x)] a b - a b g(x) f ’(x) dx.](http://images.slideplayer.com/23/6879927/slides/slide_3.jpg "Example: Evaluate 0 1 tan - 1 x dx. Example: Evaluate 1 e x ln x dx. Example: Evaluate 0 1 (2x + 3) e x dx..")
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CHAPTER 2 2.4 Continuity Integration Using Technology and Tables Example: Use the Table of Integrals to find: 2. [(4 - 3x 2 ) 0.5 / x ] dx. 3. e sin x sin 2x dx. 1. x 2 cos 3x dx.
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