∫ (from 0 to 05) of (528x+384x^2) wrt x= eching

$$\int _ { 0 } ^ { 05 } ( 528 x + 384 x ^ { 2 } ) d x =$$

Baholash

$$0$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 528x+384x^{2}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 528x\mathrm{d}x+\int 384x^{2}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$528\int x\mathrm{d}x+384\int x^{2}\mathrm{d}x$$

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. 528 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$264x^{2}+384\int x^{2}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{2}\mathrm{d}x integralni \frac{x^{3}}{3} bilan almashtiring. 384 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$264x^{2}+128x^{3}$$

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

$$264\times \left(0\times 5\right)^{2}+128\times \left(0\times 5\right)^{3}-\left(264\times 0^{2}+128\times 0^{3}\right)$$

Qisqartirish.

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