The correct option is C Undefined ∫ _ 1 ^ 4 x x ^ 2 9 dx x^2 9=t 2xdx=dt xdx=dt2 =∫ _ 8 ^ 7 dt 2t =[ ln t 2 #160; ] ...

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Substitution Method to Remove Indeterminate Form

Evaluate ∫-...

Question

Evaluate $\int_{- 1}^{4} \frac{x d x}{x^{2} - 9}$

1

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Undefined

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Solution

The correct option is C Undefined
$\int_{- 1}^{4} \frac{x}{x^{2} - 9} d x$
$x^{2} - 9 = t$
$2 x d x = d t$
$x d x = \frac{d t}{2}$
$= \int_{- 8}^{7} \frac{d t}{2 t}$
$= {[\frac{l n t}{2}]}_{- 8}^{7}$
$= {[\frac{l n (x^{2} - 9)}{9}]}_{- 1}^{4}$
$= \frac{l n 7 - l n 8}{2} \to \infty$
=undefined

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