Category: Integral Calculus
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Evaluate
Solution:
First, let's examine the numerator and denominator if they can factor or not. Since the denominator can be factored, the above item can be written as
Next, split the denominator's factors into a single factor, we have
where A, B, and C are constants and we have to determine the unknown given constants. Multiply each sides by their Least Common Denominator (LCD) which is x(x - 2)(x + 2).
Equate each term, we have
For x2:
(equation 1)For x:
(equation 2)For x0:
(equation 3)From equation 3,
From equation 2,
Substitute the values of A and B in equation 1, we have
Substitute the value of C in equation 2, we have
Therefore,
