Qosimov f. M. Qosimova m. M

3- Mavzu. Integrallarni hisoblash
1-masala. Quyidagi funksiyalarni boshlang`ich funksiyasini toping.

a) y(x)= 4∙x³ -6∙x²-4∙x+3

b) y(x)= 4∙sin(3∙x-1)

Yechish:

a) F(x)= x⁴ – x³ – x² +3x+C=x⁴-2x³-2x²+3x+C

Haqiqatdan ham, ta`rifga ko`ra

F′ (x) =y(x) shartni qanoatlantirishi kerak
F′ (x)= (x⁴-2x³-2x²+3x+C)′ = (x⁴)′ - (2x³)′ - (2x²)′ + (3x)′ + (C)′=4x³ – 6x²-4x+3

b) Mazkur funksiyaning boshlang`ich funksiyasi

F(x)= – cos (3x-1)+C ga teng.

Haqiqatdan ham,

F′ (x) =[ – cos (3x-1)+C]′ = (– cos(3x-1))′+ (C)′ =

= – ( cos(3x-1))′ + 0 = – (–sin (3x-1))∙(3x-1)′ =

= sin (3x-1)∙3 = 4sin (3x-1)

2- masala. Aniq integrallarni hisoblang.

a) ; b)

Yechish. Topshiriqni bajarishda integrallash qoidalari va formulalaridan foydalanamiz.

a)

b)