∫ (from 1 to 27) of 2pix(27x^3) wrt x eching

$$\int _ { 1 } ^ { 27 } 2 \pi x ( 27 x ^ { 3 } ) d x$$

Baholash

$$\frac{774840924\pi }{5}\approx 486846910,90782547$$

Yechim qadamlari

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

$$\int _{1}^{27}2\pi x^{4}\times 27\mathrm{d}x$$

54 hosil qilish uchun 2 va 27 ni ko'paytirish.

$$\int _{1}^{27}54\pi x^{4}\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int 54\pi x^{4}\mathrm{d}x$$

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

$$54\pi \int x^{4}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{4}\mathrm{d}x integralni \frac{x^{5}}{5} bilan almashtiring.

$$54\pi \times \frac{x^{5}}{5}$$

Qisqartirish.

$$\frac{54\pi x^{5}}{5}$$

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

$$\frac{54}{5}\pi \times 27^{5}-\frac{54}{5}\pi \times 1^{5}$$

Qisqartirish.

$$\frac{774840924\pi }{5}$$