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Question

$$\displaystyle \int_{-1}^{1} \dfrac {\sqrt {1 + x + x^{2}} - \sqrt {1 - x + x^{2}}}{\sqrt {1 + x + x^{2}} + \sqrt {1 - x + x^{2}}} dx $$


A
3π2
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B
π2
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C
0
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D
1
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Solution

The correct option is C $$0$$
 $$f(x)= \dfrac {\sqrt {1 + x + x^{2}} - \sqrt {1 - x + x^{2}}}{\sqrt {1 + x + x^{2}} + \sqrt {1 - x + x^{2}}}  $$
$$f(-x)=\dfrac {\sqrt {1 - x + x^{2}} - \sqrt {1 + x + x^{2}}}{\sqrt {1 - x + x^{2}} + \sqrt {1 + x + x^{2}}} =-f(x)$$
Since, $$ f(x)=-f(-x)$$  this is an odd function so answer will be $$0$$.

Mathematics

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