Issolvi ∫ (from 0 to 11) of 625left(11-yright)10 wrt y

$$\int_{ 0 }^{ 11 } 625 \left( 11-y \right) 10 d y$$

Evalwa

$$378125$$

Passi tas-Soluzzjonijiet

Immultiplika 625 u 10 biex tikseb 6250.

$$\int _{0}^{11}6250\left(11-y\right)\mathrm{d}y$$

Uża l-propjetà distributtiva biex timmultiplika 6250 b'11-y.

$$\int _{0}^{11}68750-6250y\mathrm{d}y$$

L-ewwel evalwa l-integru indefinit.

$$\int 68750-6250y\mathrm{d}y$$

Tintegra s-somma terminu b'terminu.

$$\int 68750\mathrm{d}y+\int -6250y\mathrm{d}y$$

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

$$\int 68750\mathrm{d}y-6250\int y\mathrm{d}y$$

Sib l-integru ta' 68750 billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}y=ay.

$$68750y-6250\int y\mathrm{d}y$$

Minn \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int y\mathrm{d}y ma' \frac{y^{2}}{2}. Immultiplika -6250 b'\frac{y^{2}}{2}.

$$68750y-3125y^{2}$$

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

$$68750\times 11-3125\times 11^{2}-\left(68750\times 0-3125\times 0^{2}\right)$$

Issimplifika.

$$378125$$