定積分・広義積分計算機

この計算機は、定積分（すなわち上下限のある積分）を、広義積分も含めて、解法手順を示しながら計算を試みます。

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 $$$\int_{-1}^{1}\left( b d m o x \right)dx$$$

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

$$$\left(\frac{b d m o x^{2}}{2}\right)|_{\left(x=1\right)}=\frac{b d m o}{2}$$$

$$$\left(\frac{b d m o x^{2}}{2}\right)|_{\left(x=-1\right)}=\frac{b d m o}{2}$$$

$$$\int_{-1}^{1}\left( b d m o x \right)dx=\left(\frac{b d m o x^{2}}{2}\right)|_{\left(x=1\right)}-\left(\frac{b d m o x^{2}}{2}\right)|_{\left(x=-1\right)}=0$$$

Answer: $$$\int_{-1}^{1}\left( b d m o x \right)dx=0$$$

Please try a new game Rotatly

定積分・広義積分計算機

定積分と広義積分を手順を追って計算する

Solution