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。

Enter a function:

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.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: calculate $$$\int_{0}^{1000}\left( - x + e^{x} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\left(- x + e^{x}\right)d x}=- \frac{x^{2}}{2} + e^{x}$$$ (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.

$$$\left(- \frac{x^{2}}{2} + e^{x}\right)|_{\left(x=1000\right)}=-500000 + e^{1000}$$$

$$$\left(- \frac{x^{2}}{2} + e^{x}\right)|_{\left(x=0\right)}=1$$$

$$$\int_{0}^{1000}\left( - x + e^{x} \right)dx=\left(- \frac{x^{2}}{2} + e^{x}\right)|_{\left(x=1000\right)}-\left(- \frac{x^{2}}{2} + e^{x}\right)|_{\left(x=0\right)}=-500001 + e^{1000}$$$

Answer: $$$\int_{0}^{1000}\left( - x + e^{x} \right)dx=-500001 + e^{1000}\approx 1.97007111401705 \cdot 10^{434}$$$

Please try a new game Rotatly

定積分與廣義積分計算器

逐步計算定積分與瑕積分

Solution