What is the integral from-pi to pi of 2x^4 ?

The integral from-pi to pi of 2x^4 is (4pi^5)/5

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integral from-pi to pi of 2x^4

\int_{- π}^{π} 2 x^{4} d x

\frac{4 π ^{5}}{5}

Decimal

244.81574 \dots

Solution steps

\int_{- π}^{π} 2 x^{4} d x

Take the constant out:

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

= 2 \cdot \int_{- π}^{π} x^{4} d x

Apply the Power Rule

: [\frac{x ^{5}}{5}]_{- π}^{π}

= 2 [\frac{x ^{5}}{5}]_{- π}^{π}

Compute the boundaries:

2 \cdot \frac{π ^{5}}{5}

= 2 \cdot 2 \cdot \frac{π ^{5}}{5}

Simplify

= \frac{4 π ^{5}}{5}

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What is the integral from-pi to pi of 2x^4 ?
The integral from-pi to pi of 2x^4 is (4pi^5)/5