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 $$$\int_{11}^{12}\left( x^{2} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{x^{2} d x}=\frac{x^{3}}{3}$$$ (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.

$$$\left(\frac{x^{3}}{3}\right)|_{\left(x=12\right)}=576$$$

$$$\left(\frac{x^{3}}{3}\right)|_{\left(x=11\right)}=\frac{1331}{3}$$$

$$$\int_{11}^{12}\left( x^{2} \right)dx=\left(\frac{x^{3}}{3}\right)|_{\left(x=12\right)}-\left(\frac{x^{3}}{3}\right)|_{\left(x=11\right)}=\frac{397}{3}$$$

Answer: $$$\int_{11}^{12}\left( x^{2} \right)dx=\frac{397}{3}\approx 132.333333333333$$$

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정적분 및 가적분 계산기

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Solution