∫ (from 3 to 5) of (3/y)2piy wrt y eching

$$\int _ { 3 } ^ { 5 } ( \frac { 3 } { y } ) 2 \pi y d y$$

Baholash

$$12\pi \approx 37,699111843$$

Yechim qadamlari

\frac{3}{y}\times 2 ni yagona kasrga aylantiring.

$$\int _{3}^{5}\frac{3\times 2}{y}\pi y\mathrm{d}y$$

\frac{3\times 2}{y}\pi ni yagona kasrga aylantiring.

$$\int _{3}^{5}\frac{3\times 2\pi }{y}y\mathrm{d}y$$

y va y ni qisqartiring.

$$\int _{3}^{5}3\times 2\pi \mathrm{d}y$$

6 hosil qilish uchun 3 va 2 ni ko'paytirish.

$$\int _{3}^{5}6\pi \mathrm{d}y$$

Avval noaniq integralni baholang.

$$\int 6\pi \mathrm{d}y$$

\int a\mathrm{d}y=ay umumiy integrallar qoidasi jadvalidan foydalanib, 6\pi integralini toping.

$$6\pi y$$

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

$$6\pi \times 5-6\pi \times 3$$

Qisqartirish.

$$12\pi$$