Mathematics, 26.02.2020 05:59, jocelynbarraza
Use both the trapezoid rule and Simpson's rule with n = 6 to approximate the arc length of the curve y = e^x^2 for x from 0 to 1.
(a) Trapezoid rule
(b) Simpson's rule
Answers: 1
![P= [0, 0.176, 0.333, 0.5, 0.667, 0.833, 1]](/tpl/images/0524/7105/7f3fd.png)
for each interval (See the attachment 1)![\int\limits^0_1 {e^{x^{2} } } \, dx =(1-0[\frac{f(0)+2[f(0.167)+f(0.133)+f(0.5)+f(0.667)+f(0.833)]+f(1)}{2(6)}\\\int\limits^0_1 {e^{x^{2} } } \, dx=1.457](/tpl/images/0524/7105/f548d.png)
![P_{m}= [0.083, 0.25, 0.417, 0.583, 0.75, 0.917]](/tpl/images/0524/7105/5961d.png)
(See the attachment 2)![\int\limits^0_1 {e^{x^{2} } } \, dx =(1-0)[\frac{f(0)+4[f(0.083)+f(0.25)+...+f(0.917)]+2[f(0.167)+f(0.333)+...+f(0.833)]+f(1]]}{6(6)} \\\int\limits^0_1 {e^{x^{2} } } \, dx =1.463](/tpl/images/0524/7105/ee6c3.png)
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