정적분 및 가적분 계산기

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

Enter a function:

Integrate with respect to:

Enter a lower limit:

If you need `-oo`, type -inf.

Enter an upper limit:

If you need `oo`, type inf.

Please write without any differentials such as `dx`, `dy` etc.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: calculate $$$\int_{-1}^{2}\left( - t \right)dt$$$

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

$$$\left(- \frac{t^{2}}{2}\right)|_{\left(t=2\right)}=-2$$$

$$$\left(- \frac{t^{2}}{2}\right)|_{\left(t=-1\right)}=- \frac{1}{2}$$$

$$$\int_{-1}^{2}\left( - t \right)dt=\left(- \frac{t^{2}}{2}\right)|_{\left(t=2\right)}-\left(- \frac{t^{2}}{2}\right)|_{\left(t=-1\right)}=- \frac{3}{2}$$$

Answer: $$$\int_{-1}^{2}\left( - t \right)dt=- \frac{3}{2}=-1.5$$$

Please try a new game Rotatly

정적분 및 가적분 계산기

정적분과 광의적분을 단계별로 계산하세요

Solution