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प्रश्न
Evaluate the following : `int_(-3)^(3) x^3/(9 - x^2)*dx`
उत्तर
Let I = `int_(-3)^(3) x^3/(9 - x^2)*dx`
Let f(x) = `x^3/(9 - x^2)`
∴ f( –x) = `(-x)^3/(9 - (- x)^2`
= `(-x^3)/(9 - x^2)`
= `-f(x)`
∴ f is an odd function.
∴ `int_-3^3 f(x)*dx = 0, "i.e." int_-3^3 x^3/(9 - x^2)*dx` = 0.
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