∫ _{-pi/2}^frac{pi{2}}(Hcosx) wrt x eching

$$\int _ { - \frac { \pi } { 2 } } ^ { \frac { \pi } { 2 } } ( H \cos x ) d x$$

Baholash

$$2H$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int H\cos(x)\mathrm{d}x$$

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

$$H\int \cos(x)\mathrm{d}x$$

Natijani olish uchun umumiy integrallar jadvalidagi \int \cos(H)\mathrm{d}H=\sin(H) integralidan foydalaning.

$$H\sin(x)$$

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

$$H\sin(\frac{1}{2}\pi )-H\sin(-\frac{1}{2}\pi )$$

Qisqartirish.

$$2H$$

H ga nisbatan hosilani topish

$$2$$