# 関数の左端点近似計算機

## 解決

$\int\limits_{a}^{b} f{\left(x \right)}\, dx\approx \Delta x \left(f{\left(x_{0} \right)} + f{\left(x_{1} \right)} + f{\left(x_{2} \right)}+\dots+f{\left(x_{n-2} \right)} + f{\left(x_{n-1} \right)}\right)$

ここで$\Delta x = \frac{b - a}{n}$

$f{\left(x \right)} = \sqrt{\cos^{4}{\left(x \right)} + 2}$, $a = 0$$b = 4$$n = 5$あります。

したがって、 $\Delta x = \frac{4 - 0}{5} = \frac{4}{5}$

$\left[0, 4\right]$を、次のエンドポイントを持つ長さ$\Delta x = \frac{4}{5}$ $n = 5$サブ間隔に分割し$a = 0$, $\frac{4}{5}$, $\frac{8}{5}$, $\frac{12}{5}$, $\frac{16}{5}$, $4 = b$

ここで、サブインターバルの左側の端点で関数を評価します。

$f{\left(x_{0} \right)} = f{\left(0 \right)} = \sqrt{3}\approx 1.732050807568877$

$f{\left(x_{1} \right)} = f{\left(\frac{4}{5} \right)} = \sqrt{\cos^{4}{\left(\frac{4}{5} \right)} + 2}\approx 1.495196773630485$

$f{\left(x_{2} \right)} = f{\left(\frac{8}{5} \right)} = \sqrt{\cos^{4}{\left(\frac{8}{5} \right)} + 2}\approx 1.414213819387789$

$f{\left(x_{3} \right)} = f{\left(\frac{12}{5} \right)} = \sqrt{\cos^{4}{\left(\frac{12}{5} \right)} + 2}\approx 1.515144715776502$

$f{\left(x_{4} \right)} = f{\left(\frac{16}{5} \right)} = \sqrt{\cos^{4}{\left(\frac{16}{5} \right)} + 2}\approx 1.730085700215823$

## 答え

$\int\limits_{0}^{4} \sqrt{\cos^{4}{\left(x \right)} + 2}\, dx\approx 6.309353453263581$A