정적분 및 가적분 계산기

이 계산기는 단계별 풀이를 보여 주면서 상한과 하한이 있는 정적분(진정적분 포함)을 계산하려고 시도합니다.

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

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정적분 및 가적분 계산기

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Solution