MAC 2312 Lecture 1: Lectures 1-10
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Fxn wlin a fxn u sub inner fxn. Lecture 2: techniques for integration: integration by parts, part ii. Use the acronym ipet as a guide for choosing u in the order of: i = inverse func. (ex. arctan(x), ln(x)) (one ibp at a time, p = polynomial (ex. 5x3: e = exponential func. (ex. ax, e3x) (sometimes 2 ibps, t = trigonometric func. (ex. cos(2x), sin(x)) (e & t interchangeable in this case) Evaluate z ln xdx. (x ln x x + c) ex. Evaluate z 1 (x arctan x ln( 1 + x2) = /4 (1/2) ln 2) Z ex sin xdx. ([ex(sin x cos x)]/2 + c) Sexsinxdx = exsinx ecosxifexfsnddyt ggg t x # same now stop. Using integration by parts: for integrals of the form. Z xn ln x dx,z xn arcsin ax dx,z xn arctan ax dx.