∫ (from a to x) of x*f(t)dt eching

$$\int _ { a } ^ { x } x \cdot f ( t ) d t$$

Baholash

$$\frac{fx\left(x^{2}-a^{2}\right)}{2}$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int xft\mathrm{d}t$$

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

$$xf\int t\mathrm{d}t$$

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

$$xf\times \frac{t^{2}}{2}$$

Qisqartirish.

$$\frac{xft^{2}}{2}$$

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

$$\frac{1}{2}xfx^{2}-\frac{1}{2}xfa^{2}$$

Qisqartirish.

$$\frac{xf\left(x-a\right)\left(x+a\right)}{2}$$

x ga nisbatan hosilani topish

$$\frac{3fx^{2}-fa^{2}}{2}$$