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Help on query formulation
Analysis on two teaching difficulties of advanced mathematics. (Chinese)
J. Nanyang Norm. Univ. 9, No. 3, 91-93 (2010).
Summary: The concept of definite integral is defined by definition of limit, which is very ideological. According to the concept of definite integral, computing the limit of sum of infinite terms with techniques for computing definite integral is teaching difficulty. Here is a way that is easy to master. The word “parts" from integration by parts means to divide $uv$, the product of two functions $u(x)$ and $v(x)$, into the sum of $\int udv$ and $\int vdu$, that is $uv=\int udv+\int vdu$. Computing infinite integral like $\int e^{ax}\sin bxdx$, $\int\sin(\ln x)dx$ is teaching difficulty. The basis of computing that kind of infinite integral is there is a obvious linear relationship like $λ\int udv+μ\int vdu=w(x)$ $(λ,μ$ are constants, $λ\neμ)$ between $\int udv$ and $\int vdu$.
Classification: I54 I55