∫ (from -1 to 1) of 1-y^2-y^2-1 wrt y eching

$$\int_{ -1 }^{ 1 } 1- { y }^{ 2 } - { y }^{ 2 } -1 d y$$

Baholash

$$-\frac{4}{3}\approx -1,333333333$$

Yechim qadamlari

-2y^{2} ni olish uchun -y^{2} va -y^{2} ni birlashtirish.

$$\int _{-1}^{1}1-2y^{2}-1\mathrm{d}y$$

0 olish uchun 1 dan 1 ni ayirish.

$$\int _{-1}^{1}-2y^{2}\mathrm{d}y$$

Avval noaniq integralni baholang.

$$\int -2y^{2}\mathrm{d}y$$

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

$$-2\int y^{2}\mathrm{d}y$$

k\neq -1 uchun integral \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} boʻlgani uchun, \int y^{2}\mathrm{d}y integralni \frac{y^{3}}{3} bilan almashtiring.

$$-\frac{2y^{3}}{3}$$

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

$$-\frac{2}{3}\times 1^{3}+\frac{2}{3}\left(-1\right)^{3}$$

Qisqartirish.

$$-\frac{4}{3}$$