Alıs¸tırmalar IV, SOS 129 (2016
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Alıştırmalar IV, SOS 129 (2016-17 Güz) 1. Aşağıdaki belirsiz integralleri gerekirse değişken (d) değiştirerek hesaplayın. (a) x3 − 4x2 + (b) (c) (f) (g) (h) (i) 2 dx 1 dx x2 (e) (f) (b) (c) x3 ln x dx x3 x(x + 1) dx x−1 √ dx x (h) ln x dx x2 x sin2 x dx 3xe−x dx (i) 4 − x2 dx √ sin( x) dx 2 2 x sin(x ) dx 3. Aşağıdaki belirli integralleri hesaplayın. cos(2πx) dx sin(2πx) sec2 tan x dx (x2 + 2)2 dx cos 3x dx esin 3x (a) (b) (d) 3 sec x dx π/2 cos x dx 0 (c) 2. Aşağıdaki belirsiz integralleri kısmi intergal (e) yöntemiyle hesaplayın. (a) (g) (d) (e) √ Özer Öztürk 1 1 + u2 du −1 1 x3 e−2x dx 0 π/2 x sin 2x dx 0 4 √ x x + 3 dx 1 4. Türkçeye çevirin: 2 x sin x dx sin2 x dx “And what are these Fluxions? The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?” http://mat.msgsu.edu.tr/∼ozer/sos129.html • ozer.ozturk@msgsu.edu.tr Sayfa 1 / 1