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

The integral from 0 to 2pi of t^2sqrt(2) is (8sqrt(2)pi^3)/3

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integral from 0 to 2pi of t^2sqrt(2)

\int_{0}^{2 π} t^{2} 2 d t

\frac{8 2 π ^{3}}{3}

Decimal Notation

116.93199 \dots

Solution steps

\int_{0}^{2 π} t^{2} 2 d t

Take the constant out:

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

= 2 \cdot \int_{0}^{2 π} t^{2} d t

Apply the Power Rule

: [\frac{t ^{3}}{3}]_{0}^{2 π}

= 2 [\frac{t ^{3}}{3}]_{0}^{2 π}

Compute the boundaries:

\frac{8 π ^{3}}{3}

= 2 \frac{8 π ^{3}}{3}

Simplify

= \frac{8 2 π ^{3}}{3}

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What is the integral from 0 to 2pi of t^2sqrt(2) ?
The integral from 0 to 2pi of t^2sqrt(2) is (8sqrt(2)pi^3)/3