MATH128 Study Guide - Quiz Guide: Antiderivative, Trigonometric Substitution, Water Skiing
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0 e e arctan arctan dx dx d dx d dx x arctan ) Total is 50: solve the following integrals, 1. The integral of the derivative of a function is that function. Let z = xex; dz = (x+1) ex, z(0) = 0 e0 = 0 and z(ln2) = ln 2eln2 =2 ln 2 = ln 4. Use ivp; let u = (ln x)2 and dv = dx, so du = 2 (ln x)/x dx and v = x. 10 dx dx dx dz (ln dx arctan arctan. 2ln e x e e e e x x x xe. 0 x x x z z x x (ln. 3 et zdz zdz y y t 2. Let z = y; z2 = y, dz = dy/ y zdz = dy. Let z = -t2, dz = -2t dt, t3 = (-1/2)zdz, so. 4 x x x e x x x.
