Review Note
Last Update: 10/05/2024 09:24 AM
Current Deck: 25考研高等数学公式+概念+定理+典例【5.0版】【数二版】【latex精制版】::04一元函数积分学::07定积分的计算
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问题
利用区间再现公式计算定积分2
\(\displaystyle\int_{a}^{b} f(x) \mathrm{d} x=\frac{1}{2} \displaystyle\int_{a}^{b}[f(x)+f(a+b-x)] \mathrm{d} x .\)
\(\displaystyle\int_{a}^{b} f(x) \mathrm{d} x=\frac{1}{2} \displaystyle\int_{a}^{b}[f(x)+f(a+b-x)] \mathrm{d} x .\)
答案
由结论1\(\displaystyle\int_{a}^{b} f(x) \mathrm{d} x=\displaystyle\int_{a}^{b} f(a+b-x) \mathrm{d} x .\)
两边相加即可的上式
\(\displaystyle\int_{a}^{b} f(x) \mathrm{d} x=\frac{1}{2} \displaystyle\int_{a}^{b}[f(x)+f(a+b-x)] \mathrm{d} x .\)
两边相加即可的上式
\(\displaystyle\int_{a}^{b} f(x) \mathrm{d} x=\frac{1}{2} \displaystyle\int_{a}^{b}[f(x)+f(a+b-x)] \mathrm{d} x .\)
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