Belirli ve Uygunsuz İntegral Hesaplayıcı

Hesaplayıcı, uygunsuz olanlar da dahil olmak üzere belirli (yani sınırları olan) integrali adımları göstererek hesaplamaya çalışacaktır.

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.

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Solution

Your input: calculate $$$\int_{0}^{2 \pi}\left( \cos{\left(x \right)} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\cos{\left(x \right)} d x}=\sin{\left(x \right)}$$$ (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.

$$$\left(\sin{\left(x \right)}\right)|_{\left(x=2 \pi\right)}=0$$$

$$$\left(\sin{\left(x \right)}\right)|_{\left(x=0\right)}=0$$$

$$$\int_{0}^{2 \pi}\left( \cos{\left(x \right)} \right)dx=\left(\sin{\left(x \right)}\right)|_{\left(x=2 \pi\right)}-\left(\sin{\left(x \right)}\right)|_{\left(x=0\right)}=0$$$

Answer: $$$\int_{0}^{2 \pi}\left( \cos{\left(x \right)} \right)dx=0$$$

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Belirli ve Uygunsuz İntegral Hesaplayıcı

Belirli ve uygunsuz integralleri adım adım hesaplayın

Solution