Issolvi ∫ (from 0 to 2) of (5438x)(18/25x)

$$\int _ { 0 } ^ { 2 } ( 5438 x ) ( 18 / 25 x )$$

Evalwa

$$\frac{261024}{25}=10440.96$$

Passi tas-Soluzzjonijiet

Immultiplika x u x biex tikseb x^{2}.

$$\int _{0}^{2}5438x^{2}\times \frac{18}{25}\mathrm{d}x$$

Esprimi 5438\times \frac{18}{25} bħala frazzjoni waħda.

$$\int _{0}^{2}\frac{5438\times 18}{25}x^{2}\mathrm{d}x$$

Immultiplika 5438 u 18 biex tikseb 97884.

$$\int _{0}^{2}\frac{97884}{25}x^{2}\mathrm{d}x$$

L-ewwel evalwa l-integru indefinit.

$$\int \frac{97884x^{2}}{25}\mathrm{d}x$$

Iffattura ‘l barra l-kostanti bl-użu ta' \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{97884\int x^{2}\mathrm{d}x}{25}$$

Minn \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int x^{2}\mathrm{d}x ma' \frac{x^{3}}{3}.

$$\frac{32628x^{3}}{25}$$

L-integru definit huwa l-antiderivattiv tal-espressjoni evalwata fil-limitu superjuri tal-integrazzjoni minus l-antiderivattiv evalwat fil-limitu inferjuri tal-integrazzjoni.

$$\frac{32628}{25}\times 2^{3}-\frac{32628}{25}\times 0^{3}$$

Issimplifika.

$$\frac{261024}{25}$$