∫ (from 4 to 9) of 1/sqrt{x wrt x eching

$$\int _ { 4 } ^ { 9 } \frac { 1 } { \sqrt { x } } d x$$

Baholash

$$2$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int \frac{1}{\sqrt{x}}\mathrm{d}x$$

\frac{1}{\sqrt{x}} ni x^{-\frac{1}{2}} sifatida qaytadan yozish. k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{-\frac{1}{2}}\mathrm{d}x integralni \frac{x^{\frac{1}{2}}}{\frac{1}{2}} bilan almashtiring. Soddalashtiring va eksponensialdan ildiz shaklga aylantiring.

$$2\sqrt{x}$$

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

$$2\times 9^{\frac{1}{2}}-2\times 4^{\frac{1}{2}}$$

Qisqartirish.

$$2$$