{1}{{(x-a)(x-b)}} - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.4
Integrate the functions in Exercises 86 to 108.

Question : 100 of 271

Marks: +1, -0

\frac{1}{\sqrt{(x-a)(x-b)}}

Solution:

Let

I=\int\frac{dx}{\sqrt{(x-a)(x-b)}}

=\int\frac{dx}{\sqrt{x^2-(a+b)x+ab}}

=\int\frac{dx}{\sqrt{x^2-2\left(\frac{a+b}{2}\right)x+\left(\frac{a+b}{2}\right)^2+ab-\left(\frac{a+b}{2}\right)^2}}

=\int\frac{dx}{\sqrt{\left(x-\left(\frac{a+b}{2}\right)^2\right)-\left(\frac{a-b}{2}\right)^2}}

=\log\left| \left(x-\frac{a+b}{2}\right) + \sqrt{\left(x-\left(\frac{a+b}{2}\right)^2\right)-\left(\frac{a-b}{2}\right)^2} \right| + C

=\log{|(x- {a+b}/2) +√{(x-a)(x-b)}|}+C

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