Issolvi ∫ (from 0 to 4) of (-74+13.25x)(-0.125) wrt x

$$\int_{ 0 }^{ 4 } (-74+13.25x)(-0.125) d x$$

Evalwa

$$23.75$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika -74+13.25x b'-0.125.

$$\int _{0}^{4}9.25-1.65625x\mathrm{d}x$$

L-ewwel evalwa l-integru indefinit.

$$\int 9.25-\frac{53x}{32}\mathrm{d}x$$

Tintegra s-somma terminu b'terminu.

$$\int 9.25\mathrm{d}x+\int -\frac{53x}{32}\mathrm{d}x$$

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

$$\int 9.25\mathrm{d}x-\frac{53\int x\mathrm{d}x}{32}$$

Sib l-integru ta' 9.25 billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}x=ax.

$$\frac{37x}{4}-\frac{53\int x\mathrm{d}x}{32}$$

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 -1.65625 b'\frac{x^{2}}{2}.

$$\frac{37x}{4}-\frac{53x^{2}}{64}$$

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

$$9.25\times 4-\frac{53}{64}\times 4^{2}-\left(9.25\times 0-\frac{53}{64}\times 0^{2}\right)$$

Issimplifika.

$$\frac{95}{4}$$