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
B
π2
C
0
D
1

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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