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 $$$\int_{x}^{a}\left( \frac{1}{x^{2}} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{1}{x^{2}} d x}=- \frac{1}{x}$$$ (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.

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

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

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

Answer: $$$\int_{x}^{a}\left( \frac{1}{x^{2}} \right)dx=\frac{1}{x} - \frac{1}{a}$$$

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정적분 및 가적분 계산기

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Solution