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

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

Aromātai

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Ngā Upane Otinga

Ko te maha noa iti rawa atu o 6 me 2 ko 6. Me tahuri \frac{1}{6} me \frac{1}{2} ki te hautau me te tautūnga 6.

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

Tā te mea he rite te tauraro o \frac{1}{6} me \frac{3}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 1 ki te 3, ka 4.

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

Whakahekea te hautanga \frac{4}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Me tahuri te 2 ki te hautau \frac{6}{3}.

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

Tā te mea he rite te tauraro o \frac{6}{3} me \frac{1}{3}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 6, ka 5.

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

Whakawehe \frac{2}{3} ki te \frac{5}{3} mā te whakarea \frac{2}{3} ki te tau huripoki o \frac{5}{3}.

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

Me whakarea te \frac{2}{3} ki te \frac{3}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Me whakakore tahi te 3 i te taurunga me te tauraro.

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

Ko te maha noa iti rawa atu o 2 me 6 ko 6. Me tahuri \frac{1}{2} me \frac{1}{6} ki te hautau me te tautūnga 6.

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

Tā te mea he rite te tauraro o \frac{3}{6} me \frac{1}{6}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 3, ka 2.

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

Whakahekea te hautanga \frac{2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Me whakarea te \frac{1}{3} ki te \frac{6}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\times 6}{3\times 5}.

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

Whakahekea te hautanga \frac{6}{15} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

Tangohia te \frac{2}{5} i te \frac{2}{5}, ka 0.

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

Kimihia te tau tōpū o 0 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

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Mēnā ko F\left(x\right) he pārōnaki kōaro o f\left(x\right), kāti ko te huinga o ngā pārōnaki kōaro katoa o f\left(x\right) ka whakaaturia e F\left(x\right)+C. Nō reira, me tāpiri te pūmau o te whakatōpūtanga C\in \mathrm{R} ki te otinga.

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Kimi Pārōnaki e ai ki x

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