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 $$$\int_{0}^{2}\left( 2 - e^{\frac{x}{2}} \right)dx$$$

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

$$$\left(2 \left(x - e^{\frac{x}{2}}\right)\right)|_{\left(x=2\right)}=4 - 2 e$$$

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

$$$\int_{0}^{2}\left( 2 - e^{\frac{x}{2}} \right)dx=\left(2 \left(x - e^{\frac{x}{2}}\right)\right)|_{\left(x=2\right)}-\left(2 \left(x - e^{\frac{x}{2}}\right)\right)|_{\left(x=0\right)}=6 - 2 e$$$

Answer: $$$\int_{0}^{2}\left( 2 - e^{\frac{x}{2}} \right)dx=6 - 2 e\approx 0.563436343081909$$$

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정적분 및 가적분 계산기

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Solution