∫34 dxln⁡x3>∫34 dxx3 =∫34x-1/3dx =32x2/334 =3242/3-32/3 ≅0.65

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$\int_{3}^{4} \frac{dx}{\sqrt[3]{\ln x}} =$

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$< \frac{1}{2}$

$> \frac{1}{2}$

$= \frac{1}{2}$

< 0

answer is B.

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Detailed Solution

$\int_{3}^{4} \frac{d x}{\sqrt[3]{\ln x}} > \int_{3}^{4} \frac{d x}{\sqrt[3]{x}} = \int_{3}^{4} x^{- 1 / 3} d x = \frac{3}{2} {[x^{2 / 3}]}_{3}^{4} = \frac{3}{2} [4^{2 / 3} - 3^{2 / 3}] ≅ 0.65$

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