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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Integrate with respect to:

Enter a lower limit:

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

Enter an upper limit:

If you need `oo`, type inf.

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Solution

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

First, calculate the corresponding indefinite integral: $$$\int{x^{100} d x}=\frac{x^{101}}{101}$$$ (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.

$$$\left(\frac{x^{101}}{101}\right)|_{\left(x=1\right)}=\frac{1}{101}$$$

$$$\left(\frac{x^{101}}{101}\right)|_{\left(x=-1\right)}=- \frac{1}{101}$$$

$$$\int_{-1}^{1}\left( x^{100} \right)dx=\left(\frac{x^{101}}{101}\right)|_{\left(x=1\right)}-\left(\frac{x^{101}}{101}\right)|_{\left(x=-1\right)}=\frac{2}{101}$$$

Answer: $$$\int_{-1}^{1}\left( x^{100} \right)dx=\frac{2}{101}\approx 0.0198019801980198$$$

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Solution