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mat104-bahar_odev6 - CALISMA SORULARI-6(2009-2010-Bahar...

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C ¸ ALIS ¸MA SORULARI-6 (2009-2010-Bahar) Dersin Adı: Mat104 Konu: C ¸ok Katlı ˙ Integraller 1. ˙ Integrasyon b¨olgelerini ¸ciziniz ve integralleri hesaplayınız. (a) Z π 0 Z x 0 x sin y dy dx (b) Z 1 0 Z y 2 0 3 y 3 e xy dx dy 2. f ’yi verilen b¨olgede integre ediniz. (a) 1 x 2 , 1 y 2 karesinde f ( x, y ) = 1 / ( xy ). (b) uv d¨uzleminin birinci d¨ortte bir b¨olgesinden u + v = 1 do˘grusuyla kesilen ¨u¸ cgen b¨olgede f ( u, v ) = v - u . 3. ˙ Integrasyon b¨olgesini ¸ciziniz, integrasyon sınırlarını de˘gi¸ stirerek integralleri hesaplayınız. (a) Z π 0 Z π x sin y y dy dx (b) Z 1 / 16 0 Z 1 / 2 y 1 / 4 cos (16 πx 5 ) dx dy 4. R, y = x, y = 2 x, x + y = 2 do˘grularıyla sınırlı b¨olge olmak ¨uzere, ZZ R xy dA integ- ralini hesaplayınız. 5. ¨ Ustten z = x 2 silindiri ve alttan xy d¨uzleminde y = 2 - x 2 parabol¨u ve y = x do˘grusuyla ¸cevrelenen b¨olgeyle sınırlanan cismin hacmini bulunuz. 6. Birinci sekizde bir b¨olgeden z = 4 - x 2 - y y¨uzeyiyle kesilen cismin hacmini bulunuz.
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