∫ (from 2 to 3) of 56x-x wrt x eching

$$\int_{ 2 }^{ 3 } 56x-x d x$$

Baholash

$$\frac{275}{2}=137,5$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 56x-x\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 56x\mathrm{d}x+\int -x\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$56\int x\mathrm{d}x-\int x\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring. 56 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$28x^{2}-\int x\mathrm{d}x$$

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

$$28x^{2}-\frac{x^{2}}{2}$$

Qisqartirish.

$$\frac{55x^{2}}{2}$$

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

$$\frac{55}{2}\times 3^{2}-\frac{55}{2}\times 2^{2}$$

Qisqartirish.

$$\frac{275}{2}$$