Integration by Reduction Formulae - Indefinite Integration, Class 12, Maths Class 12 Notes | EduRev

Class 12 : Integration by Reduction Formulae - Indefinite Integration, Class 12, Maths Class 12 Notes | EduRev

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F. INTEGRATION BY REDUCTION FORMULAE


Ex.47  CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration


Sol.

CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration

 

Ex.48 Integration of 1/(x2 + k)n.


Sol.

CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration
Above is the reduction formula for CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration [1/(x2 + k)n]dx . By repeated application of this formula the integral shall reduce to that of  CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration

 


Ex.49 Integrate (x + 2) / (2x2 + 4x + 3)2.


Sol. Here (d/dx) (2x2 + 4x + 3) = 4x + 4.
CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration
Now put x + 1 = t and then applying the reduction formula, we get
CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration


Ex.50 Integrate (2x + 3)/(x2 + 2x + 3)2.


Sol. Here (d/dx) (x2 + 2x + 3) = 2x + 2
CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration

CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration

Ex.51 If Im=

CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration


Sol.

CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration

Ex.52 If Im,n = CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration


Sol. We have, Im,n = CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integrationcosm x.cosnx dx
CBSE, Class 12, IIT JEE, Syllabus, Preparation, NCERT, Important, Indefinite Integration
As we have cos (n – 1) x = cos nx cos x + sin nx . sinx

Integration by Reduction Formulae - Indefinite Integration, Class 12, Maths Class 12 Notes | EduRev

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