问题

Questions in category: 重积分 (Multiple Integrals).

设 $f(x)$ 连续, 证明: $\int_0^1\mathrm{d}y\int_{0}^{\sqrt{y}}e^y f(x)\mathrm{d}x=\int_0^1(e-e^{x^2})f(x)\mathrm{d}x$.

Posted by haifeng on 2025-04-12 17:43:53 last update 2025-04-12 17:43:53 | Answers (1) | 收藏

设 $f(x)$ 连续, 证明: $\int_0^1\mathrm{d}y\int_{0}^{\sqrt{y}}e^y f(x)\mathrm{d}x=\int_0^1(e-e^{x^2})f(x)\mathrm{d}x$.