What is the integral from-2 to 1 of x^2e^{2x^3+4} ?

The integral from-2 to 1 of x^2e^{2x^3+4} is (e^6)/6-1/(6e^{12)}

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integral from-2 to 1 of x^2e^{2x^3+4}

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

\frac{e ^{6}}{6} - \frac{1}{6 e ^{12}}

Decimal

67.23813 \dots

Solution steps

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

Apply u-substitution

= \int_{\frac{1}{e ^{12}}}^{e^{6}} \frac{1}{6} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{6} u]_{\frac{1}{e ^{12}}}^{e^{6}}

Compute the boundaries:

\frac{e ^{6}}{6} - \frac{1}{6 e ^{12}}

= \frac{e ^{6}}{6} - \frac{1}{6 e ^{12}}

What is the integral from-2 to 1 of x^2e^{2x^3+4} ?
The integral from-2 to 1 of x^2e^{2x^3+4} is (e^6)/6-1/(6e^{12)}