∫ (from 0 to 11) of 625left(11-yright)10 wrt y eching

$$\int_{ 0 }^{ 11 } 625 \left( 11-y \right) 10 d y$$

Baholash

$$378125$$

Yechim qadamlari

6250 hosil qilish uchun 625 va 10 ni ko'paytirish.

$$\int _{0}^{11}6250\left(11-y\right)\mathrm{d}y$$

6250 ga 11-y ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int _{0}^{11}68750-6250y\mathrm{d}y$$

Avval noaniq integralni baholang.

$$\int 68750-6250y\mathrm{d}y$$

Summani muddatma-muddat integratsiya qiling.

$$\int 68750\mathrm{d}y+\int -6250y\mathrm{d}y$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int 68750\mathrm{d}y-6250\int y\mathrm{d}y$$

\int a\mathrm{d}y=ay umumiy integrallar qoidasi jadvalidan foydalanib, 68750 integralini toping.

$$68750y-6250\int y\mathrm{d}y$$

k\neq -1 uchun integral \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} boʻlgani uchun, \int y\mathrm{d}y integralni \frac{y^{2}}{2} bilan almashtiring. -6250 ni \frac{y^{2}}{2} marotabaga ko'paytirish.

$$68750y-3125y^{2}$$

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

$$68750\times 11-3125\times 11^{2}-\left(68750\times 0-3125\times 0^{2}\right)$$

Qisqartirish.

$$378125$$