What is the integral from-2 to-4 of (x+4)^{10} ?

The integral from-2 to-4 of (x+4)^{10} is -2048/11

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integral from-2 to-4 of (x+4)^{10}

\int_{- 2}^{- 4} (x + 4)^{10} d x

- \frac{2048}{11}

Decimal Notation

- 186.18181 \dots

Solution steps

\int_{- 2}^{- 4} (x + 4)^{10} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 4}^{- 2} (x + 4)^{10} d x

Apply u-substitution

: \int_{0}^{2} u^{10} d u

= - \int_{0}^{2} u^{10} d u

Apply the Power Rule

: [\frac{u ^{11}}{11}]_{0}^{2}

= - [\frac{u ^{11}}{11}]_{0}^{2}

Compute the boundaries:

\frac{2048}{11}

= - \frac{2048}{11}

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

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

\int_{0}^{1} x x^{2} + 3 d x

\int_{- 1}^{1} t^{3} d t

\int_{4}^{8} x d x

What is the integral from-2 to-4 of (x+4)^{10} ?
The integral from-2 to-4 of (x+4)^{10} is -2048/11