Calculatrice d’intégrales définies et impropres

La calculatrice essaiera d'évaluer l'intégrale définie (c.-à-d. avec bornes), y compris les intégrales impropres, en affichant les étapes.

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

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Solution

Your input: calculate $$$\int_{-1}^{1}\left( \operatorname{acos}{\left(x \right)} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\operatorname{acos}{\left(x \right)} d x}=x \operatorname{acos}{\left(x \right)} - \sqrt{1 - x^{2}}$$$ (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.

$$$\left(x \operatorname{acos}{\left(x \right)} - \sqrt{1 - x^{2}}\right)|_{\left(x=1\right)}=0$$$

$$$\left(x \operatorname{acos}{\left(x \right)} - \sqrt{1 - x^{2}}\right)|_{\left(x=-1\right)}=- \pi$$$

$$$\int_{-1}^{1}\left( \operatorname{acos}{\left(x \right)} \right)dx=\left(x \operatorname{acos}{\left(x \right)} - \sqrt{1 - x^{2}}\right)|_{\left(x=1\right)}-\left(x \operatorname{acos}{\left(x \right)} - \sqrt{1 - x^{2}}\right)|_{\left(x=-1\right)}=\pi$$$

Answer: $$$\int_{-1}^{1}\left( \operatorname{acos}{\left(x \right)} \right)dx=\pi\approx 3.14159265358979$$$

Calculatrice d’intégrales définies et impropres

Calculez des intégrales définies et impropres étape par étape

Solution