∫12ln[x]dx+∫23ln[x]dx+∫34ln[x]dx=∫120 dx+∫23ln2 dx+∫34ln3 dx=0+(ln2)(x)23+(ln3)(x)34=0+ln2+ln3=ln 6

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$\int_{1}^{4} \ln [x] d x =$

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$\ln 4$

$\ln 6$

$\ln 8$

$\ln 3$

answer is B.

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Detailed Solution

$\int_{1}^{2} \ln [x] d x + \int_{2}^{3} \ln [x] d x + \int_{3}^{4} \ln [x] d x = \int_{1}^{2} 0 d x + \int_{2}^{3} \ln 2 d x + \int_{3}^{4} \ln 3 d x$

$= 0 + (\ln 2) {(x)}_{2}^{3} + (\ln 3) {(x)}_{3}^{4}$

$= 0 + \ln 2 + \ln 3$

$= \ln 6$

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