∫ (from - 015 to 665) of [(-x^2+2x)-(-1+1/2x)] wrt x eching

$$\int _ { - 015 } ^ { 665 } [ ( - x ^ { 2 } + 2 x ) - ( - 1 + \frac { 1 } { 2 } x ) ] d x$$

Baholash

$$-\frac{1172330495}{12}\approx -97694207,916666667$$

Yechim qadamlari

-1+\frac{1}{2}x teskarisini topish uchun har birining teskarisini toping.

$$\int _{0\times 15}^{665}-x^{2}+2x+1-\frac{1}{2}x\mathrm{d}x$$

\frac{3}{2}x ni olish uchun 2x va -\frac{1}{2}x ni birlashtirish.

$$\int _{0\times 15}^{665}-x^{2}+\frac{3}{2}x+1\mathrm{d}x$$

0 hosil qilish uchun 0 va 15 ni ko'paytirish.

$$\int _{0}^{665}-x^{2}+\frac{3}{2}x+1\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int -x^{2}+\frac{3x}{2}+1\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int -x^{2}\mathrm{d}x+\int \frac{3x}{2}\mathrm{d}x+\int 1\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$-\int x^{2}\mathrm{d}x+\frac{3\int x\mathrm{d}x}{2}+\int 1\mathrm{d}x$$

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. -1 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$-\frac{x^{3}}{3}+\frac{3\int x\mathrm{d}x}{2}+\int 1\mathrm{d}x$$

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. \frac{3}{2} ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$-\frac{x^{3}}{3}+\frac{3x^{2}}{4}+\int 1\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 1 integralini toping.

$$-\frac{x^{3}}{3}+\frac{3x^{2}}{4}+x$$

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

$$-\frac{665^{3}}{3}+\frac{3}{4}\times 665^{2}+665-\left(-\frac{0^{3}}{3}+\frac{3}{4}\times 0^{2}+0\right)$$

Qisqartirish.

$$-\frac{1172330495}{12}$$