15_3_12 - 2-1 2 e 3-2 e ! .

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12. m = Z 1 0 ( e t + e - t ) dt = e 2 - 1 e M x = 0 = Z 1 0 e t ( e t + e - t ) dt = e 2 + 1 2 M y = 0 = Z 1 0 2 t ( e t + e - t ) dt = 2 2 ( e - 1 ) e M z = 0 = Z 1 0 e - t ( e t + e - t ) dt = 3 e 2 - 1 2 e 2 The centroid is e 3 + e 2 e 2 - 2 , 2 2 e + 1 , 3 e
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