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Question Number 75098 by Rio Michael last updated on 07/Dec/19

the function f is defined by f (x) = \frac{2}{x^{2} - 1}

a) Express f into partial fraction

b . show that \int_{3}^{5} f (x) d x = l n (\frac{4}{3})

Answered by peter frank last updated on 07/Dec/19

y = \frac{2}{(x - 1) (x + 1)}

2 = \frac{A}{x - 1} + \frac{B}{x + 1}

2 = A (x + 1) + B (x - 1)

A = 1 B = - 1

y = \int (\frac{1}{x - 1} - \frac{1}{x + 1}) d y

Missing \left or extra \right

y^{^{'}} = l n (\frac{2}{3}) - l n (\frac{1}{2}) = l n (\frac{4}{3})

Commented by Rio Michael last updated on 07/Dec/19

t h a n k s s i r