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Question
Fill in the blank : `int_(-9)^9 x^3/(4 - x^2)*dx` = _______
Solution
Let I = `int_(-9)^9 x^3/(4 - x^2)*dx`
Let f(x) = `x^3/(4 - x^2)`
∴ f(– x) = `(-x)^2/(4 - (-x)^2`
= `-x^3/(4 - x^2)`
= – f(x)
∴ f(x) is an odd function.
∴ `int_(-9)^9 x^3/(4 - x^2)*dx = 0. ...[because int_("a")^"a" f(x) = 0, if f(x) "odd function"]`
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