∫ (from 1 to 2) of (3t^2-t)dt eching

$$\int _ { 1 } ^ { 2 } ( 3 t ^ { 2 } - t ) d t$$

Baholash

$$\frac{11}{2}=5,5$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 3t^{2}-t\mathrm{d}t$$

Summani muddatma-muddat integratsiya qiling.

$$\int 3t^{2}\mathrm{d}t+\int -t\mathrm{d}t$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$3\int t^{2}\mathrm{d}t-\int t\mathrm{d}t$$

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. 3 ni \frac{t^{3}}{3} marotabaga ko'paytirish.

$$t^{3}-\int t\mathrm{d}t$$

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. -1 ni \frac{t^{2}}{2} marotabaga ko'paytirish.

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

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

$$2^{3}-\frac{2^{2}}{2}-\left(1^{3}-\frac{1^{2}}{2}\right)$$

Qisqartirish.

$$\frac{11}{2}$$