Määrättyjen ja epäoleellisten integraalien laskin

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

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Solution

Your input: calculate $$$\int_{11}^{12}\left( x^{2} \right)dx$$$

First, calculate the corresponding indefinite integral: $$$\int{x^{2} d x}=\frac{x^{3}}{3}$$$ (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.

$$$\left(\frac{x^{3}}{3}\right)|_{\left(x=12\right)}=576$$$

$$$\left(\frac{x^{3}}{3}\right)|_{\left(x=11\right)}=\frac{1331}{3}$$$

$$$\int_{11}^{12}\left( x^{2} \right)dx=\left(\frac{x^{3}}{3}\right)|_{\left(x=12\right)}-\left(\frac{x^{3}}{3}\right)|_{\left(x=11\right)}=\frac{397}{3}$$$

Answer: $$$\int_{11}^{12}\left( x^{2} \right)dx=\frac{397}{3}\approx 132.333333333333$$$

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Määrättyjen ja epäoleellisten integraalien laskin

Laske määrättyjä ja epäoleellisia integraaleja askel askeleelta

Solution