定積分與廣義積分計算器

此計算器將嘗試計算定積分（即帶有上下限的積分），包含廣義積分，並顯示步驟。

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If you need `-oo`, type -inf.

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If you need `oo`, type inf.

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Solution

Your input: calculate $$$\int_{100}^{150}\left( \frac{1}{x^{2}} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{1}{x^{2}} d x}=- \frac{1}{x}$$$ (for steps, see indefinite integral calculator)

According to the Fundamental Theorem of Calculus, $$$\int_a^b F(x) dx=f(b)-f(a)$$$, so just evaluate the integral at the endpoints, and that's the answer.

$$$\left(- \frac{1}{x}\right)|_{\left(x=150\right)}=- \frac{1}{150}$$$

$$$\left(- \frac{1}{x}\right)|_{\left(x=100\right)}=- \frac{1}{100}$$$

$$$\int_{100}^{150}\left( \frac{1}{x^{2}} \right)dx=\left(- \frac{1}{x}\right)|_{\left(x=150\right)}-\left(- \frac{1}{x}\right)|_{\left(x=100\right)}=\frac{1}{300}$$$

Answer: $$$\int_{100}^{150}\left( \frac{1}{x^{2}} \right)dx=\frac{1}{300}\approx 0.00333333333333333$$$

定積分與廣義積分計算器

逐步計算定積分與瑕積分

Solution