csat-suneung 2025 Q26C

csat-suneung · South-Korea · csat__math 3 marks Indefinite & Definite Integrals Definite Integral Evaluation (Computational)

As shown in the figure, a solid figure has as its base the region enclosed by the curve $y = \sqrt{\frac{x+1}{x(x + \ln x)}}$, the $x$-axis, and the two lines $x = 1$ and $x = e$. When the cross-section of this solid figure cut by a plane perpendicular to the $x$-axis is a square, what is the volume of this solid figure? [3 points]
(1) $\ln(e+1)$
(2) $\ln(e+2)$
(3) $\ln(e+3)$
(4) $\ln(2e+1)$
(5) $\ln(2e+2)$

As shown in the figure, a solid figure has as its base the region enclosed by the curve $y = \sqrt{\frac{x+1}{x(x + \ln x)}}$, the $x$-axis, and the two lines $x = 1$ and $x = e$. When the cross-section of this solid figure cut by a plane perpendicular to the $x$-axis is a square, what is the volume of this solid figure? [3 points]\\
(1) $\ln(e+1)$\\
(2) $\ln(e+2)$\\
(3) $\ln(e+3)$\\
(4) $\ln(2e+1)$\\
(5) $\ln(2e+2)$

Paper Questions

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