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CURSO de ENGENHARIA (MECÂNICA) – VOLTA REDONDA ... - Uff

CURSO de ENGENHARIA (MECÂNICA) – VOLTA REDONDA ... - Uff

CURSO de ENGENHARIA (MECÂNICA) – VOLTA REDONDA ... - Uff

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PROAC / COSEAC - Gabarito2 a QUESTÃO: (1,6 ponto)funçõesCalcule∫∫By = x eCálculos e respostas:∫10(x + y) dx dyx⎡ e ⎤ 1 2y⎢∫ ( x + y)dx⎥dy= xyx ∫+0⎣ ⎦2∫= 1 0∫= 1 0⎡⎛⎢⎜xe⎢⎣⎝⎡⎢xe⎢⎣xx2xe+22xe+22x⎞ ⎛⎟ ⎜−x⎠ ⎝223xdx⎥ ⎥ ⎤−2 ⎦3xy = e com 0 ≤ 12x ⎞dx⎥ ⎥ ⎤+ ⎟2⎠⎦] 1 0x x e x= xe − e + −4 2⎛2⎞⎜e 1⎟⎛ 1 ⎞= 1−1+−− ⎜0−1+− 0⎟⎝ 4 2 ⎠ ⎝ 4 ⎠212= e − +421= e +4 434xe] dxx, on<strong>de</strong> B é a região compreendida entre os gráficos das≤ x .4

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