What is the integral from-1 to 1 of x^3e^{-x^2} ?

The integral from-1 to 1 of x^3e^{-x^2} is 0

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integral from-1 to 1 of x^3e^{-x^2}

\int_{- 1}^{1} x^{3} e^{- x^{2}} d x

0

Solution steps

\int_{- 1}^{1} x^{3} e^{- x^{2}} d x

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

x^{3} e^{- x^{2}} :

Odd

= 0

\int_{- 1}^{0} (8 x - 1) d x

\int_{1}^{3} (- x^{2} + 4 x) d x

\int_{- 1}^{5} x^{2} d x

\int_{0}^{2} (x - 2)^{4} d x

\int_{0}^{b} x^{3} d x

What is the integral from-1 to 1 of x^3e^{-x^2} ?
The integral from-1 to 1 of x^3e^{-x^2} is 0