∫ (from 1 to 2) of 3/t^4dt eching

$$\int _ { 1 } ^ { 2 } \frac { 3 } { t ^ { 4 } } d t$$

Baholash

$$\frac{7}{8}=0,875$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

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

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

k\neq -1 uchun integral \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} boʻlgani uchun, \int \frac{1}{t^{4}}\mathrm{d}t integralni -\frac{1}{3t^{3}} bilan almashtiring. 3 ni -\frac{1}{3t^{3}} marotabaga ko'paytirish.

$$-\frac{1}{t^{3}}$$

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

$$-2^{-3}+1^{-3}$$

Qisqartirish.

$$\frac{7}{8}$$