5.6-bo'lim : Aniq integralning ta'rifi
11. \(x\) ga nisbatan quyidagi integralni differensiallang.
\[\int_{7}^{{\sin \left( {6x} \right)}}{{\sqrt {{t^2} + 4} dt}}\]Yechim
Bu Hisoblashning asosiy teoremasining I bo'limini tezda qo'llashdan boshqa narsa emas.
Ammo shuni yodda tutingki, yuqori chegara shunchaki \(x\) emas, chunki biz “ichki funktsiya” \(\sin \left( {6x} \right)\) kabi zanjir qoidasidan foydalanishimiz kerak.
hosilasi,
\[\frac{d}{{dx}}\left[ {\int_{7}^{{\sin \left( {6x} \right)}}{{\sqrt {{t^2} + 4} dt}}} \right] = \require{bbox} \bbox[2pt,border:1px solid black]{{6\cos \left( {6x} \right)\sqrt {{{\sin }^2}\left( {6x} \right) + 4} }}\]