∫ _{1/5}^7ln(5)x wrt x eching

$$\int_{ \frac{ 1 }{ 5 } }^{ 7 } \ln ( 5 ) x d x$$

Baholash

$$\frac{612\ln(5)}{25}\approx 39,399040096$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x\log_{e}\left(5\right)\mathrm{d}x$$

\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x yordamidan konstantani qavsdan tashqariga chiqaring.

$$\log_{e}\left(5\right)\int x\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring.

$$\log_{e}\left(5\right)\times \frac{x^{2}}{2}$$

Qisqartirish.

$$\frac{\ln(5)x^{2}}{2}$$

Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.

$$\frac{1}{2}\ln(5)\times 7^{2}-\frac{1}{2}\ln(5)\times \left(\frac{1}{5}\right)^{2}$$

Qisqartirish.

$$\frac{612\ln(5)}{25}$$