∫ _{-pi/2}^frac{pi{2}}(1+cos(x)) wrt x eching

$$\int_{ - \frac{ \pi }{ 2 } }^{ \frac{ \pi }{ 2 } } (1+ \cos ( x ) ) d x$$

Baholash

$$\pi +2\approx 5,141592654$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 1+\cos(x)\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 1\mathrm{d}x+\int \cos(x)\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 1 integralini toping.

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

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

$$x+\sin(x)$$

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

$$\frac{\pi }{2}+\sin(\frac{\pi }{2})-\left(-\frac{\pi }{2}+\sin(-\frac{\pi }{2})\right)$$

Qisqartirish.

$$\pi +2$$