MATH 41 Final: MATH 41 Stanford 09Final
15 Feb 2019
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October 31, 2014: the following questions have to do with the integral z ln(x) x3 dx (a) evaluate z ln(x) x3 dx. Use integration by parts x3 ln(x) dx = z (cid:0)x 3(cid:1) ln(x) dx = z (cid:18) . Ln(x) dx x 2 ln(x) z x 2 ln(x) +z 1. You can also do parts using u and dv: du = Z x 3 ln(x) dx = ln(x) (cid:18) . 1 x x 2 to get x 2 dx = . 4 x 2 + c (b) suppose your answer from part (a) is. Explain how to use this answer to understand if the integral z . 1 ln(x) x3 dx is convergent or divergent. ln x 4x. Assuming the answer from (a) is ln x 4x. 1 ln(x) x3 dx = (cid:18) ln x 4x. 3 ln(x) x3 dx we would then take the limit of ln t 4t. To determine z limit has indeterminate form ln t 4.
