MATH 1132Q Lecture 3: MATH 1132Q , Lecture 3 , 7.1
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Objective : find an antiderivative by using integration by parts. Example : find the derivative of f(x) = -x cos(x) + sinx + c f"(x) = (-x)(-sinx) + (-1)(cosx) + cosx. If u and v are functions of x and have continuous derivatives then . U dv = u v - v du dv = sin(x) dx v = -cos(x) * note * - pick the part for u that has a derivative that will make it simplified to something. Pick the part for dv , that when you take the antiderivative, it doesn"t get more complicated. Fill in values : u v - v du (x) (-cos(x)) - (-cos(x) (1 dx) Ln(x) dx u = ln(x) du = 1 / x dv = 1 dx v = x u v - v du (ln(x)) (x) - ( x ) (1 / x ) dx x ln(x) - 1 dx. Cancel out x ln(x) - x + c.
