∫ (from 1 to 100) of 4/x^3 eching

$$\int _ { 1 } ^ { 100 } \frac { 4 } { x ^ { 3 } }$$

Baholash

$$\frac{9999}{5000}=1,9998$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int \frac{4}{x^{3}}\mathrm{d}x$$

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

$$4\int \frac{1}{x^{3}}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int \frac{1}{x^{3}}\mathrm{d}x integralni -\frac{1}{2x^{2}} bilan almashtiring. 4 ni -\frac{1}{2x^{2}} marotabaga ko'paytirish.

$$-\frac{2}{x^{2}}$$

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

$$-2\times 100^{-2}+2\times 1^{-2}$$

Qisqartirish.

$$\frac{9999}{5000}$$