Match the following

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Match the following.
Column IColumn II
(A) ∫01(1+2008x2008)ex2008dx\int_{0}^{1} (1 + 2008 x^{2008}) e^{x^{2008}} dx equals(p) e−1e^{-1}
(B) The value of the definite integral ∫01e−x2dx+∫1e−ln⁡xdx\int_{0}^{1} e^{-x^2} dx + \int_{1}^{e} \sqrt{-\ln x} dx is equal to(q) e−1/4e^{-1/4}
(C) lim⁡n→∞(1!⋅22⋅33⋯(n−1)n−1⋅nnn1+2+3+⋯+n)1/n2\lim_{n \to \infty} \left( \frac{1! \cdot 2^2 \cdot 3^3 \cdots (n-1)^{n-1} \cdot n^n}{n^{1+2+3+\dots+n}} \right)^{1/n^2} equals(r) e1/2e^{1/2}
(s) ee

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