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

The integral from-1 to 1 of x^2e^{x^3} is (e^2-1)/(3e)

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

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

\frac{e ^{2} - 1}{3 e}

Decimal

0.78346 \dots

Solution steps

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

Apply u-substitution

= \int_{- 1}^{1} \frac{e ^{u}}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{- 1}^{1} e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{3} [e^{u}]_{- 1}^{1}

Compute the boundaries:

e - \frac{1}{e}

= \frac{1}{3} (e - \frac{1}{e})

Simplify

= \frac{e ^{2} - 1}{3 e}

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