What is the integral from 0 to 2pi of 5t*sqrt(2) ?

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

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integral from 0 to 2pi of 5t*sqrt(2)

\int_{0}^{2 π} 5 t \cdot 2 d t

102 π^{2}

Decimal Notation

139.57728 \dots

Solution steps

\int_{0}^{2 π} 5 t 2 d t

Take the constant out:

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

= 52 \cdot \int_{0}^{2 π} t d t

Apply the Power Rule

: [\frac{t ^{2}}{2}]_{0}^{2 π}

= 52 [\frac{t ^{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 5t*sqrt(2) ?
The integral from 0 to 2pi of 5t*sqrt(2) is 10sqrt(2)pi^2