,
a>0 va k=0 bo‘lganda esa
natijalarni olamiz.
Masalan,
.
Endi a<0 holni ko‘ramiz. Bu holda kvadrat uchhad diskriminanti D>0 deb olishimiz kerak, chunki aks holda barcha nuqtalarda ax2+bx+c≤0 va I2 integral ostidagi funksiya aniqlanmagan bo‘ladi. Bu shartda
.
Endi umumiyroq ko‘rinishdagi quyidagi integrallarni qaraymiz:
.
Oldin I3 integralni hisoblash yo‘lini ko‘rsatamiz:
![](data:image/png;base64,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) .
Bu yerda I1 yuqorida ko‘rib o‘tilgan integraldir va uni hisoblashni bilamiz.
Misol sifatida ushbu integralni qaraymiz:
.
I4 integral ham shu kabi hisoblanadi:
.
Bu yerdagi I2 integralni hisoblash usuli yuqorida ko‘rsatilgan edi.
I4 ko‘rinishdagi integralni hisoblashga misol keltiramiz:
.
0>
Do'stlaringiz bilan baham: |