What is the integral from 0 to 2pi of 5xsqrt(2) ?

The integral from 0 to 2pi of 5xsqrt(2) is 10sqrt(2)pi^2

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integral from 0 to 2pi of 5xsqrt(2)

\int_{0}^{2 π} 5 x 2 d x

102 π^{2}

Solution steps

\int_{0}^{2 π} 5 x 2 d x

Take the constant out:

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

= 52 \cdot \int_{0}^{2 π} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{2 π}

= 52 [\frac{x ^{2}}{2}]_{0}^{2 π}

Compute the boundaries:

2 π^{2}

= 52 \cdot 2 π^{2}

Simplify

= 102 π^{2}

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What is the integral from 0 to 2pi of 5xsqrt(2) ?
The integral from 0 to 2pi of 5xsqrt(2) is 10sqrt(2)pi^2