∫ (from 0 to pi) of (7sin(t)-9cos(t))dt eching

$$\int _ { 0 } ^ { \pi } ( 7 \sin ( t ) - 9 \cos ( t ) ) d t$$

Baholash

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Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 7\sin(t)-9\cos(t)\mathrm{d}t$$

Summani muddatma-muddat integratsiya qiling.

$$\int 7\sin(t)\mathrm{d}t+\int -9\cos(t)\mathrm{d}t$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$7\int \sin(t)\mathrm{d}t-9\int \cos(t)\mathrm{d}t$$

Natijani olish uchun umumiy integrallar jadvalidagi \int \sin(t)\mathrm{d}t=-\cos(t) integralidan foydalaning. 7 ni -\cos(t) marotabaga ko'paytirish.

$$-7\cos(t)-9\int \cos(t)\mathrm{d}t$$

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

$$-7\cos(t)-9\sin(t)$$

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

$$-7\cos(\pi )-9\sin(\pi )-\left(-7\cos(0)-9\sin(0)\right)$$

Qisqartirish.

$$14$$