∫ (from 50 to 100) of y(x) wrt x eching

$$\int_{ 50 }^{ 100 } y(x) d x$$

Baholash

$$3750y$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int yx\mathrm{d}x$$

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

$$y\int x\mathrm{d}x$$

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.

$$y\times \frac{x^{2}}{2}$$

Qisqartirish.

$$\frac{yx^{2}}{2}$$

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

$$\frac{1}{2}y\times 100^{2}-\frac{1}{2}y\times 50^{2}$$

Qisqartirish.

$$3750y$$

y ga nisbatan hosilani topish

$$3750$$