Määrättyjen ja epäoleellisten integraalien laskin

Laskin yrittää laskea määrätyn (eli rajoilla varustetun) integraalin, mukaan lukien epäoleelliset tapaukset, ja näyttää välivaiheet.

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Integrate with respect to:

Enter a lower limit:

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

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If you need `oo`, type inf.

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Solution

Your input: calculate $$$\int_{-3}^{5}\left( \cos{\left(x \right)} \right)dx$$$

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.

$$$\left(\sin{\left(x \right)}\right)|_{\left(x=5\right)}=\sin{\left(5 \right)}$$$

$$$\left(\sin{\left(x \right)}\right)|_{\left(x=-3\right)}=- \sin{\left(3 \right)}$$$

$$$\int_{-3}^{5}\left( \cos{\left(x \right)} \right)dx=\left(\sin{\left(x \right)}\right)|_{\left(x=5\right)}-\left(\sin{\left(x \right)}\right)|_{\left(x=-3\right)}=\sin{\left(5 \right)} + \sin{\left(3 \right)}$$$

Answer: $$$\int_{-3}^{5}\left( \cos{\left(x \right)} \right)dx=\sin{\left(5 \right)} + \sin{\left(3 \right)}\approx -0.817804266603271$$$

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Määrättyjen ja epäoleellisten integraalien laskin

Laske määrättyjä ja epäoleellisia integraaleja askel askeleelta

Solution