∫ (from 0 to 1) of 2^2(2x)*(2x) wrt x eching

$$\int _ { 0 } ^ { 1 } 2 ^ { 2 } ( 2 x ) \cdot ( 2 x ) d x$$

Baholash

$$\frac{16}{3}\approx 5,333333333$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\int _{0}^{1}2^{3}x\times 2x\mathrm{d}x$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 1 ni qo‘shib, 4 ni oling.

$$\int _{0}^{1}2^{4}xx\mathrm{d}x$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\int _{0}^{1}2^{4}x^{2}\mathrm{d}x$$

4 daraja ko‘rsatkichini 2 ga hisoblang va 16 ni qiymatni oling.

$$\int _{0}^{1}16x^{2}\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int 16x^{2}\mathrm{d}x$$

\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x yordamidan konstantani qavsdan tashqariga chiqaring.

$$16\int x^{2}\mathrm{d}x$$

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.

$$\frac{16x^{3}}{3}$$

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

$$\frac{16}{3}\times 1^{3}-\frac{16}{3}\times 0^{3}$$

Qisqartirish.

$$\frac{16}{3}$$