Issolvi ∫ (from 0 to 2) of (24+24x+06x^2)(x) wrt x

$$\int_{ 0 }^{ 2 } (24+24x+06 { x }^{ 2 } )(x) d x$$

Evalwa

$$112$$

Passi tas-Soluzzjonijiet

Immultiplika 0 u 6 biex tikseb 0.

$$\int _{0}^{2}\left(24+24x+0x^{2}\right)x\mathrm{d}x$$

Xi ħaġa mmultiplikata b'żero jirriżulta f'żero.

$$\int _{0}^{2}\left(24+24x+0\right)x\mathrm{d}x$$

Żid 24 u 0 biex tikseb 24.

$$\int _{0}^{2}\left(24+24x\right)x\mathrm{d}x$$

Uża l-propjetà distributtiva biex timmultiplika 24+24x b'x.

$$\int _{0}^{2}24x+24x^{2}\mathrm{d}x$$

L-ewwel evalwa l-integru indefinit.

$$\int 24x+24x^{2}\mathrm{d}x$$

Tintegra s-somma terminu b'terminu.

$$\int 24x\mathrm{d}x+\int 24x^{2}\mathrm{d}x$$

Iffattura ‘l barra l-kostanti f’kull wieħed minn dawn it-termini.

$$24\int x\mathrm{d}x+24\int x^{2}\mathrm{d}x$$

Minn \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int x\mathrm{d}x ma' \frac{x^{2}}{2}. Immultiplika 24 b'\frac{x^{2}}{2}.

$$12x^{2}+24\int x^{2}\mathrm{d}x$$

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}. Immultiplika 24 b'\frac{x^{3}}{3}.

$$12x^{2}+8x^{3}$$

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

$$12\times 2^{2}+8\times 2^{3}-\left(12\times 0^{2}+8\times 0^{3}\right)$$

Issimplifika.

$$112$$