What is the integral from-4 to 0 of x^3sqrt(256-x^4) ?

The integral from-4 to 0 of x^3sqrt(256-x^4) is -2048/3

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integral from-4 to 0 of x^3sqrt(256-x^4)

\int_{- 4}^{0} x^{3} 256 - x^{4} d x

- \frac{2048}{3}

Decimal Notation

- 682.66666 \dots

Solution steps

\int_{- 4}^{0} x^{3} 256 - x^{4} d x

Apply u-substitution

: \int_{0}^{256} - \frac{u}{4} d u

= \int_{0}^{256} - \frac{u}{4} d u

Take the constant out:

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

= - \frac{1}{4} \cdot \int_{0}^{256} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{256}

= - \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{256}

Compute the boundaries:

\frac{8192}{3}

= - \frac{1}{4} \cdot \frac{8192}{3}

Simplify

= - \frac{2048}{3}

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

\int_{x}^{1} y d y

\int_{- 5}^{1} \frac{1}{5 - 4 x} d x

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

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

What is the integral from-4 to 0 of x^3sqrt(256-x^4) ?
The integral from-4 to 0 of x^3sqrt(256-x^4) is -2048/3