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laiz [17]
2 years ago
12

Find ∫^[infinity]_-[infinity] xe^-x^2 dx.

Mathematics
1 answer:
mote1985 [20]2 years ago
3 0

Answer:

Zero

Step-by-step explanation:

We are to find

\int\limits^{infinity} _{-infinity} xe^-x^2 dx.

Here the integral is of the form x varying from negative to positive

And negative limit = positive limit in dimension

Let us assume f(x) =xe^{-x^2}

A function is odd if f(x) = -f(-x) and even if f(x) = f(-x)

Let us check f(-x) = -f(x)

So f is an odd function.

As per properties of integration, we have

\int\limits^a_{-a}  {f(x)} \, dx=0 if fis an odd function.

Our function f is odd and a = infinity

So we can apply this rule to find out the

integral value is zero.

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