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.

Please write without any differentials such as `dx`, `dy` etc.

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Solution

Your input: calculate $$$\int_{11}^{12}\left( 2 x \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{2 x d x}=x^{2}$$$ (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.

$$$\left(x^{2}\right)|_{\left(x=12\right)}=144$$$

$$$\left(x^{2}\right)|_{\left(x=11\right)}=121$$$

$$$\int_{11}^{12}\left( 2 x \right)dx=\left(x^{2}\right)|_{\left(x=12\right)}-\left(x^{2}\right)|_{\left(x=11\right)}=23$$$

Answer: $$$\int_{11}^{12}\left( 2 x \right)dx=23$$$

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定積分與廣義積分計算器

逐步計算定積分與瑕積分

Solution