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We define the error function erf(x) byerf x =2Z x0ex2dx.We can prove that lim x+erf x = 1, which means thatZ 0ex2dx = limb Z b0ex2dx =2limberf b =2,Z...

We define the error function erf(x) byerf x =2√πZ x0e−x2dx.We can prove that lim x→+∞erf x = 1, which means thatZ ∞0e−x2dx = limb→∞ Z b0e−x2dx =√π2limb→∞erf b =√π2,Z ∞−∞e−x2dx = 2 Z ∞0e−x2dx =√π.(a) (4 pts) Find the indefinite integralZx2e−x2dxas a function involving erf(x). (Hint: you will need to use integration by parts). SEE ATTACHED FILE

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