Issolvi ∫ (from 0 to 2) of (-3.6x+0.5x^2)(-0.1x) wrt x

$$\int_{ 0 }^{ 2 } (-3.6x+0.5 { x }^{ 2 } )(-0.1x) d x$$

Evalwa

$$0.76$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika -3.6x+0.5x^{2} b'-0.1.

$$\int _{0}^{2}\left(0.36x-0.05x^{2}\right)x\mathrm{d}x$$

Uża l-propjetà distributtiva biex timmultiplika 0.36x-0.05x^{2} b'x.

$$\int _{0}^{2}0.36x^{2}-0.05x^{3}\mathrm{d}x$$

L-ewwel evalwa l-integru indefinit.

$$\int \frac{9x^{2}}{25}-\frac{x^{3}}{20}\mathrm{d}x$$

Tintegra s-somma terminu b'terminu.

$$\int \frac{9x^{2}}{25}\mathrm{d}x+\int -\frac{x^{3}}{20}\mathrm{d}x$$

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

$$\frac{9\int x^{2}\mathrm{d}x}{25}-\frac{\int x^{3}\mathrm{d}x}{20}$$

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 0.36 b'\frac{x^{3}}{3}.

$$\frac{3x^{3}}{25}-\frac{\int x^{3}\mathrm{d}x}{20}$$

Minn \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} għal k\neq -1, issostitwixxi \int x^{3}\mathrm{d}x ma' \frac{x^{4}}{4}. Immultiplika -0.05 b'\frac{x^{4}}{4}.

$$\frac{3x^{3}}{25}-\frac{x^{4}}{80}$$

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

$$\frac{3}{25}\times 2^{3}-\frac{2^{4}}{80}-\left(\frac{3}{25}\times 0^{3}-\frac{0^{4}}{80}\right)$$

Issimplifika.

$$\frac{19}{25}$$