Issolvi ∫ (from 2 to 3) of (82^3+3z-1) wrt z=

$$\int _ { 2 } ^ { 3 } ( 82 ^ { 3 } + 3 z - 1 ) d z =$$

Evalwa

$$\frac{1102749}{2}=551374.5$$

Passi tas-Soluzzjonijiet

Ikkalkula 82 bil-power ta' 3 u tikseb 551368.

$$\int _{2}^{3}551368+3z-1\mathrm{d}z$$

Naqqas 1 minn 551368 biex tikseb 551367.

$$\int _{2}^{3}551367+3z\mathrm{d}z$$

L-ewwel evalwa l-integru indefinit.

$$\int 551367+3z\mathrm{d}z$$

Tintegra s-somma terminu b'terminu.

$$\int 551367\mathrm{d}z+\int 3z\mathrm{d}z$$

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

$$\int 551367\mathrm{d}z+3\int z\mathrm{d}z$$

Sib l-integru ta' 551367 billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}z=az.

$$551367z+3\int z\mathrm{d}z$$

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

$$551367z+\frac{3z^{2}}{2}$$

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

$$551367\times 3+\frac{3}{2}\times 3^{2}-\left(551367\times 2+\frac{3}{2}\times 2^{2}\right)$$

Issimplifika.

$$\frac{1102749}{2}$$