137_1314_Test4_Solutions - MAT137Y1 Calculus Test 3 Solutions February 5th 2014 1 Calculate x3 ex dx We do integration by parts three times Each time we

137_1314_Test4_Solutions - MAT137Y1 Calculus Test 3...

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MAT137Y1 - Calculus! Test 3 – Solutions February 5th, 2014 1.CalculateWe do integration by parts three times. Each time we takedv=exanduasthe rest. Z x 3 e x dx Z x 3 e x dx = x 3 e x - Z 3 x 2 e x dx = x 3 e x - 3 x 2 e x + Z 6 xe x dx = x 3 e x - 3 x 2 e x + 6 xe x - Z 6 e x dx = x 3 e x - 3 x 2 e x + 6 xe x - 6 e x + C = ( x 3 - 3 x 2 + 6 x - 6 ) e x + C
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