∫ (from 0 to 4) of (2x^2-525x)(1-0125(x)) wrt x eching

$$\int_{ 0 }^{ 4 } (2 { x }^{ 2 } -525x)(1-0125(x)) d x$$

Baholash

$$-\frac{12472}{3}\approx -4157,333333333$$

Yechim qadamlari

0 hosil qilish uchun 0 va 125 ni ko'paytirish.

$$\int _{0}^{4}\left(2x^{2}-525x\right)\left(1-0x\right)\mathrm{d}x$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$\int _{0}^{4}\left(2x^{2}-525x\right)\left(1-0\right)\mathrm{d}x$$

1 olish uchun 1 dan 0 ni ayirish.

$$\int _{0}^{4}\left(2x^{2}-525x\right)\times 1\mathrm{d}x$$

2x^{2}-525x ga 1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int _{0}^{4}2x^{2}-525x\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int 2x^{2}-525x\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 2x^{2}\mathrm{d}x+\int -525x\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$2\int x^{2}\mathrm{d}x-525\int x\mathrm{d}x$$

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

$$\frac{2x^{3}}{3}-525\int x\mathrm{d}x$$

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. -525 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$\frac{2x^{3}}{3}-\frac{525x^{2}}{2}$$

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

$$\frac{2}{3}\times 4^{3}-\frac{525}{2}\times 4^{2}-\left(\frac{2}{3}\times 0^{3}-\frac{525}{2}\times 0^{2}\right)$$

Qisqartirish.

$$-\frac{12472}{3}$$