The correct option is A 0 Let, #160; I = ∫_ 2^2xdx/(1+x^4)(1+x^2) Now using ∫_a^bf(x)dx = ∫_a^bf(a+b x)dx I = ∫_ 2^2( x)dx/(1+( x)^4)(1+ ...

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Integration of Piecewise Continuous Functions

∫-22xdx/1+x41...

Question

$\int_{- 2}^{2} \frac{x d x}{(1 + x^{4}) (1 + x^{2})} =$

\frac{π}{4}

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0

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\frac{π}{12}

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\frac{π}{24}

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Solution

The correct option is A $0$
Let, $I = \int_{- 2}^{2} \frac{x d x}{(1 + x^{4}) (1 + x^{2})}$
Now using $\int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x$
$I = \int_{- 2}^{2} \frac{(- x) d x}{(1 + {(- x)}^{4}) (1 + {(- x)}^{2})} = - \int_{- 2}^{2} \frac{x d x}{(1 + x^{4}) (1 + x^{2})} = - I$
$\Rightarrow I + I = 0 \Rightarrow I = 0$

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