∫ (8/7-1/2)^2+(3/4-3/7)^2 eching

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

Baholash

$$\frac{405x}{784}+С$$

Yechim qadamlari

\frac{9}{14} olish uchun \frac{8}{7} dan \frac{1}{2} ni ayirish.

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

2 daraja ko‘rsatkichini \frac{9}{14} ga hisoblang va \frac{81}{196} ni qiymatni oling.

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

\frac{9}{28} olish uchun \frac{3}{4} dan \frac{3}{7} ni ayirish.

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

2 daraja ko‘rsatkichini \frac{9}{28} ga hisoblang va \frac{81}{784} ni qiymatni oling.

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

\frac{405}{784} olish uchun \frac{81}{196} va \frac{81}{784}'ni qo'shing.

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, \frac{405}{784} integralini toping.

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

Агар F\left(x\right)f\left(x\right) ning dastlabki holati boʻlsa, u holatda f\left(x\right) ning barcha dastlabki holatlari toʻplami F\left(x\right)+C tarafidan belgilanadi. Shu sababli natijaga C\in \mathrm{R} integrallash konstantasini qoʻshing.

$$\frac{405x}{784}+С$$

x ga nisbatan hosilani topish

$$\frac{405}{784} = 0,5165816326530612$$