Two Integral Problems
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Introduction
These are two Integral Problems in our textbook. It’s a little difficult but very interesting. Let’s see.
Problems
Exercise 1
For the more information about the following problem, you can refer to the book Mathematical-analysis-III of Nankai University Exercise 15(B)-12(4).
研究下列广义积分的敛散性：
\[\int_{\Omega}\frac{1}{\displaystyle\sum_{i=1}^{n}\left|x_i\right|^p_i}dx_1...dx_n,p_i>0,i=1,2,...,n\] \[\textbf{(a)}\Omega:\sum_{i=1}^{n}\left|x_i\right|\leq1\] \[\textbf{(b)}\Omega:\sum_{i=1}^{n}\left|x_i\right|\gt1\]Exercise 2
For the more information about the following problem, you can refer to the book Mathematical-analysis-III of Nankai University Exercise 15(B)-15.
设(\mathbf{A}=(a_{ij}))是(n)阶实对称正定矩阵，$b_1,…,b_n$和$c$均是实数.求
\[I=\int_{\mathbb{R}^n}\exp\left(-\sum_{i,j=1}^{n}a_{ij}x_ix_j+2\sum_{i=1}^{n}b_ix_i+c\right)dx_1...dx_n\]其中$\exp(u)$表示$e^u$.
Solution for PDF
Click Here and get the solution about these two Integral Problems.
Remark
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