Q. 44.0( 2 Votes )

Evaluate the following integrals:


Answer :

Consider


Expressing the integral




Consider


Let and split,




Consider


Let




We know that



Now consider



By partial fraction decomposition,



1 = A (x – 2) + B (x – 3)


1 = Ax – 2A + Bx – 3B


1 = (A + B) x – (2A + 3B)


A + B = 0 and 2A + 3B = -1


Solving the two equations,


2A + 2B = 0


2A + 3B = -1


-B = 1


B = -1 and A = 1




Consider


Let u = x – 3 dx = du



We know that



Similarly


Let u = x – 2 dx = du



We know that



Then,




Then,





Then,



We know that






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