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 $$$\int_{-1}^{2}\left( 13 t^{4} \right)dt$$$

First, calculate the corresponding indefinite integral: $$$\int{13 t^{4} d t}=\frac{13 t^{5}}{5}$$$ (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.

$$$\left(\frac{13 t^{5}}{5}\right)|_{\left(t=2\right)}=\frac{416}{5}$$$

$$$\left(\frac{13 t^{5}}{5}\right)|_{\left(t=-1\right)}=- \frac{13}{5}$$$

$$$\int_{-1}^{2}\left( 13 t^{4} \right)dt=\left(\frac{13 t^{5}}{5}\right)|_{\left(t=2\right)}-\left(\frac{13 t^{5}}{5}\right)|_{\left(t=-1\right)}=\frac{429}{5}$$$

Answer: $$$\int_{-1}^{2}\left( 13 t^{4} \right)dt=\frac{429}{5}\approx 85.8$$$

정적분 및 가적분 계산기

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Solution