The given definite integration is a special integration ,
erf(x)=π1∫−xxe−t2dt=π2∫0xe−t2dt∫−xxe−t2dt=2π∫−xxπ2e−t2dt
Now, use this concept and our integration will be
∫−∞∞e−x2dx=2π∫−∞∞π2e−x2dx=2π⋅[erf(x)]−∞∞=2π⋅2=π Therefore, the option C is the right answer.
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