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Popular >

integral from-2 to 0 of x^2e^{x^3+8}

Solution

\int_{- 2}^{0} x^{2} e^{x^{3} + 8} d x

Solution

\frac{e ^{8} - 1}{3}

+1

Decimal Notation

993.31932 \dots

Solution steps

\int_{- 2}^{0} x^{2} e^{x^{3} + 8} d x

Apply u-substitution

: \int_{0}^{8} \frac{e ^{u}}{3} d u

= \int_{0}^{8} \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_{0}^{8} e^{u} d u

Use the common integral:

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

= \frac{1}{3} [e^{u}]_{0}^{8}

Compute the boundaries:

e^{8} - 1

= \frac{1}{3} (e^{8} - 1)

Simplify

= \frac{e ^{8} - 1}{3}

Popular Examples

integral of 2/(1+cos(2x))

\int \frac{2}{1 + cos ( 2 x )} d x

integral of (x-1)(x+1)

\int (x - 1) (x + 1) d x

integral of x^3(2x^4+4)^2

\int x^{3} (2 x^{4} + 4)^{2} d x

integral of (arctan(x))/(x^2+1)

\int \frac{arctan ( x )}{x ^{2} + 1} d x

taylor e^x,2 taylor

e^{x}, 2

Frequently Asked Questions (FAQ)

What is the integral from-2 to 0 of x^2e^{x^3+8} ?
The integral from-2 to 0 of x^2e^{x^3+8} is (e^8-1)/3