Määrättyjen ja epäoleellisten integraalien laskin

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

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 $$$\int_{x}^{a}\left( \frac{1}{x^{2}} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{\frac{1}{x^{2}} d x}=- \frac{1}{x}$$$ (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.

$$$\left(- \frac{1}{x}\right)|_{\left(x=a\right)}=- \frac{1}{a}$$$

$$$\left(- \frac{1}{x}\right)|_{\left(x=x\right)}=- \frac{1}{x}$$$

$$$\int_{x}^{a}\left( \frac{1}{x^{2}} \right)dx=\left(- \frac{1}{x}\right)|_{\left(x=a\right)}-\left(- \frac{1}{x}\right)|_{\left(x=x\right)}=\frac{1}{x} - \frac{1}{a}$$$

Answer: $$$\int_{x}^{a}\left( \frac{1}{x^{2}} \right)dx=\frac{1}{x} - \frac{1}{a}$$$

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Määrättyjen ja epäoleellisten integraalien laskin

Laske määrättyjä ja epäoleellisia integraaleja askel askeleelta

Solution