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SalasSV_08_highlights

# SalasSV_08_highlights - 8.9 INTEGRAL CURVES SEPARABLE...

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CHAPTER HIGHLIGHTS 8.1 Integral Tables and Review Important integral formulas (p. 446) A table of integral appears on the inside covers. 8.2 Integration by Parts u dv = uv v du . (p. 451) Success with the technique depends on choosing u and dv so that vdu is easier to integrate than udv . The integral of ln x and the integrals of the inverse trigono- metric functions are calculated using integration by parts (p. 453). 8.3 Powers and Products of Trigonometric Functions Integrals of the form sin m x cos n x dx can be calculated by using the basic identity sin 2 x cos 2 x = 1 and the double-angle formulas for sine and cosine Reduction formulas: sin n x dx = − 1 n sin n 1 x cos x + n 1 n sin n 2 x dx , cos n x dx = 1 n cos n 1 x sin x + n 1 n cos n 2 x dx . The main tools for calculating such integrals as tan m x sec n x dx are the identities 1 + tan 2 x = sec 2 x and integration by parts. 8.4 Integrals Involving a 2 x 2 , a 2 + x 2 , x 2 a 2 + x 2 a 2 a 2
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