Question

19£®¸ù¾Ý¶¨»ý·ÖµÄ¶¨Ò壬${¡Ò}_{0}^{2}$x²dxµÈÓÚ£¨¡¡¡¡£©

• A£® $\sum_{i=1}^{n}$£¨$\frac{i-1}{n}$£©²•$\frac{1}{n}$
• B£® $\underset{lim}{n¡ú¡Þ}$$\sum_{i=1}^{n}$£¨$\frac{i-1}{n}$£©²•$\frac{1}{n}$
• C£® $\sum_{i=1}^{n}$£¨$\frac{2i}{n}$£©²•$\frac{2}{n}$
• D£® $\underset{lim}{n¡ú¡Þ}$$\sum_{i=1}^{n}$£¨$\frac{2i}{n}$£©²•$\frac{2}{n}$

Answer 1

·ÖÎö ¸ù¾Ý¶¨»ý·ÖµÄ¶¨Òå¼´¿ÉÇó³ö£®

½â´ð ½â£º[0£¬2]nµÈ·Ö£¬·ÖµãΪx_i=$\frac{2i}{n}$£¬£¨i=1£¬2£¬3£¬¡­£¬n£©£¬
СÇø¼ä[x_i-1£¬x_i]µÄ³¤¶È¡÷x_i=$\frac{2}{n}$£¬È¡${¦Î}_{{\;}_{i}}$=x_i£¬£¨i=1£¬2£¬3£¬¡­£¬n£©£¬
$\sum_{i=1}^{n}$f£¨${¦Î}_{{\;}_{i}}$£©¡÷x_i=$\sum_{i=1}^{n}$${¦Î}_{{\;}_{i}}$²¡÷x_i=$\sum_{i=1}^{n}$x_i²¡÷x_i=$\sum_{i=1}^{n}$£¨$\frac{2i}{n}$£©²£¨$\frac{2}{n}$£©£¬
¡à${¡Ò}_{0}^{2}$x²dx=$\underset{lim}{n¡ú¡Þ}$=$\sum_{i=1}^{n}$£¨$\frac{2i}{n}$£©²£¨$\frac{2}{n}$£©£¬
¹ÊÑ¡£ºD£®

µãÆÀ ±¾Ì⿼²éÁ˶¨»ý·ÖµÄ¶¨Ò壬ÊôÓÚ»ù´¡Ì⣮