∫ (from r to sqrt { alpha ^ 2) of - r}r wrt z eching

$$\int _ { r } ^ { \sqrt { \alpha ^ { 2 } - r } } r d z$$

Baholash

$$r\left(\sqrt{\alpha ^{2}-r}-r\right)$$

$$r\leq \alpha ^{2}$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int r\mathrm{d}z$$

\int a\mathrm{d}z=az umumiy integrallar qoidasi jadvalidan foydalanib, r integralini toping.

$$rz$$

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

$$r\left(\alpha ^{2}-r\right)^{\frac{1}{2}}-rr$$

Qisqartirish.

$$r\left(\sqrt{\alpha ^{2}-r}-r\right)$$

r ga nisbatan hosilani topish

$$\frac{\alpha ^{2}}{\sqrt{\alpha ^{2}-r}}-2r-\frac{3r}{2\sqrt{\alpha ^{2}-r}}$$