Whakaoti i te ∫ (+5/42)+(-3/21)+(+4/28)+(-2/63)=

$$\int ( + \frac { 5 } { 42 } ) + ( - \frac { 3 } { 21 } ) + ( + \frac { 4 } { 28 } ) + ( - \frac { 2 } { 63 } ) =$$

Aromātai

$$\frac{11x}{126}+С$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{3}{21} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\int \frac{5}{42}-\frac{1}{7}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Ko te maha noa iti rawa atu o 42 me 7 ko 42. Me tahuri \frac{5}{42} me \frac{1}{7} ki te hautau me te tautūnga 42.

$$\int \frac{5}{42}-\frac{6}{42}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Tā te mea he rite te tauraro o \frac{5}{42} me \frac{6}{42}, me tango rāua mā te tango i ō raua taurunga.

$$\int \frac{5-6}{42}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Tangohia te 6 i te 5, ka -1.

$$\int -\frac{1}{42}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Whakahekea te hautanga \frac{4}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\int -\frac{1}{42}+\frac{1}{7}-\frac{2}{63}\mathrm{d}x$$

Ko te maha noa iti rawa atu o 42 me 7 ko 42. Me tahuri -\frac{1}{42} me \frac{1}{7} ki te hautau me te tautūnga 42.

$$\int -\frac{1}{42}+\frac{6}{42}-\frac{2}{63}\mathrm{d}x$$

Tā te mea he rite te tauraro o -\frac{1}{42} me \frac{6}{42}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\int \frac{-1+6}{42}-\frac{2}{63}\mathrm{d}x$$

Tāpirihia te -1 ki te 6, ka 5.

$$\int \frac{5}{42}-\frac{2}{63}\mathrm{d}x$$

Ko te maha noa iti rawa atu o 42 me 63 ko 126. Me tahuri \frac{5}{42} me \frac{2}{63} ki te hautau me te tautūnga 126.

$$\int \frac{15}{126}-\frac{4}{126}\mathrm{d}x$$

Tā te mea he rite te tauraro o \frac{15}{126} me \frac{4}{126}, me tango rāua mā te tango i ō raua taurunga.

$$\int \frac{15-4}{126}\mathrm{d}x$$

Tangohia te 4 i te 15, ka 11.

$$\int \frac{11}{126}\mathrm{d}x$$

Kimihia te tau tōpū o \frac{11}{126} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{11x}{126}$$

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.

$$\frac{11x}{126}+С$$

Kimi Pārōnaki e ai ki x

$$\frac{11}{126} = 0.0873015873015873$$