∫ (from 3 to 4) of (t^2+t)dt eching

$$\int _ { 3 } ^ { 4 } ( t ^ { 2 } + t ) d t$$

Baholash

$$\frac{95}{6}\approx 15,833333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int t^{2}+t\mathrm{d}t$$

Summani muddatma-muddat integratsiya qiling.

$$\int t^{2}\mathrm{d}t+\int t\mathrm{d}t$$

k\neq -1 uchun integral \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} boʻlgani uchun, \int t^{2}\mathrm{d}t integralni \frac{t^{3}}{3} bilan almashtiring.

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

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

$$\frac{t^{3}}{3}+\frac{t^{2}}{2}$$

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

$$\frac{4^{3}}{3}+\frac{4^{2}}{2}-\left(\frac{3^{3}}{3}+\frac{3^{2}}{2}\right)$$

Qisqartirish.

$$\frac{95}{6}$$