Whakaoti i te ∫ (8/7-1/2)^2+(3/4-3/7)^2

$$\int ( \frac { 8 } { 7 } - \frac { 1 } { 2 } ) ^ { 2 } + ( \frac { 3 } { 4 } - \frac { 3 } { 7 } ) ^ { 2 }$$

Aromātai

$$\frac{405x}{784}+С$$

Ngā Upane Otinga

Tangohia te \frac{1}{2} i te \frac{8}{7}, ka \frac{9}{14}.

$$\int \left(\frac{9}{14}\right)^{2}+\left(\frac{3}{4}-\frac{3}{7}\right)^{2}\mathrm{d}x$$

Tātaihia te \frac{9}{14} mā te pū o 2, kia riro ko \frac{81}{196}.

$$\int \frac{81}{196}+\left(\frac{3}{4}-\frac{3}{7}\right)^{2}\mathrm{d}x$$

Tangohia te \frac{3}{7} i te \frac{3}{4}, ka \frac{9}{28}.

$$\int \frac{81}{196}+\left(\frac{9}{28}\right)^{2}\mathrm{d}x$$

Tātaihia te \frac{9}{28} mā te pū o 2, kia riro ko \frac{81}{784}.

$$\int \frac{81}{196}+\frac{81}{784}\mathrm{d}x$$

Tāpirihia te \frac{81}{196} ki te \frac{81}{784}, ka \frac{405}{784}.

$$\int \frac{405}{784}\mathrm{d}x$$

Kimihia te tau tōpū o \frac{405}{784} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{405x}{784}$$

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.

$$\frac{405x}{784}+С$$

Kimi Pārōnaki e ai ki x

$$\frac{405}{784} = 0.5165816326530612$$