Issolvi ∫ (1/6+1/2):(2-1/3)-(1/2-frac{1}{6})*frac{6}{5}

$$\int ( \frac { 1 } { 6 } + \frac { 1 } { 2 } ) : ( 2 - \frac { 1 } { 3 } ) - ( \frac { 1 } { 2 } - \frac { 1 } { 6 } ) \times \frac { 6 } { 5 }$$

Evalwa

$$С$$

Passi tas-Soluzzjonijiet

L-inqas multipli komuni ta' 6 u 2 huwa 6. Ikkonverti \frac{1}{6} u \frac{1}{2} fi frazzjonijiet bid-denominatur 6.

$$\int \frac{\frac{1}{6}+\frac{3}{6}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Billi \frac{1}{6} u \frac{3}{6} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\int \frac{\frac{1+3}{6}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Żid 1 u 3 biex tikseb 4.

$$\int \frac{\frac{4}{6}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Naqqas il-frazzjoni \frac{4}{6} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\int \frac{\frac{2}{3}}{2-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Ikkonverti 2 fi frazzjoni \frac{6}{3}.

$$\int \frac{\frac{2}{3}}{\frac{6}{3}-\frac{1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Billi \frac{6}{3} u \frac{1}{3} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\int \frac{\frac{2}{3}}{\frac{6-1}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Naqqas 1 minn 6 biex tikseb 5.

$$\int \frac{\frac{2}{3}}{\frac{5}{3}}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Iddividi \frac{2}{3} b'\frac{5}{3} billi timmultiplika \frac{2}{3} bir-reċiproku ta' \frac{5}{3}.

$$\int \frac{2}{3}\times \frac{3}{5}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Immultiplika \frac{2}{3} b'\frac{3}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\int \frac{2\times 3}{3\times 5}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Annulla 3 fin-numeratur u d-denominatur.

$$\int \frac{2}{5}-\left(\frac{1}{2}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

L-inqas multipli komuni ta' 2 u 6 huwa 6. Ikkonverti \frac{1}{2} u \frac{1}{6} fi frazzjonijiet bid-denominatur 6.

$$\int \frac{2}{5}-\left(\frac{3}{6}-\frac{1}{6}\right)\times \frac{6}{5}\mathrm{d}x$$

Billi \frac{3}{6} u \frac{1}{6} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\int \frac{2}{5}-\frac{3-1}{6}\times \frac{6}{5}\mathrm{d}x$$

Naqqas 1 minn 3 biex tikseb 2.

$$\int \frac{2}{5}-\frac{2}{6}\times \frac{6}{5}\mathrm{d}x$$

Naqqas il-frazzjoni \frac{2}{6} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\int \frac{2}{5}-\frac{1}{3}\times \frac{6}{5}\mathrm{d}x$$

Immultiplika \frac{1}{3} b'\frac{6}{5} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\int \frac{2}{5}-\frac{1\times 6}{3\times 5}\mathrm{d}x$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{1\times 6}{3\times 5}.

$$\int \frac{2}{5}-\frac{6}{15}\mathrm{d}x$$

Naqqas il-frazzjoni \frac{6}{15} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\int \frac{2}{5}-\frac{2}{5}\mathrm{d}x$$

Naqqas \frac{2}{5} minn \frac{2}{5} biex tikseb 0.

$$\int 0\mathrm{d}x$$

Sib l-integru ta' 0 billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}x=ax.

$$0$$

Jekk F\left(x\right) huwa antiderivattiv ta' f\left(x\right), allura s-sett tal-antiderivati kollha ta' f\left(x\right) jingħata minn F\left(x\right)+C. Għalhekk, żid il-kostanti ta' integrazzjoni C\in \mathrm{R} mar-riżultat.

$$С$$

Iddifferenzja w.r.t. x

$$0$$