What is the integral from 0 to 2pi of 8tsqrt(2) ?

The integral from 0 to 2pi of 8tsqrt(2) is 16sqrt(2)pi^2

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integral from 0 to 2pi of 8tsqrt(2)

\int_{0}^{2 π} 8 t 2 d t

162 π^{2}

Decimal

223.32365 \dots

Solution steps

\int_{0}^{2 π} 8 t 2 d t

Take the constant out:

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

= 82 \cdot \int_{0}^{2 π} t d t

Apply the Power Rule

: [\frac{t ^{2}}{2}]_{0}^{2 π}

= 82 [\frac{t ^{2}}{2}]_{0}^{2 π}

Compute the boundaries:

2 π^{2}

= 82 \cdot 2 π^{2}

Simplify

= 162 π^{2}

\int_{- 1}^{1} (2 - x^{2})^{\frac{3}{2}} d x

\int_{0}^{r} (a r^{3} + b r) 2 π r d r

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

\int_{2}^{\infty} x^{- 2} d x

\int_{0}^{1} \frac{( - x + 1 ) ^{2}}{2} d x

What is the integral from 0 to 2pi of 8tsqrt(2) ?
The integral from 0 to 2pi of 8tsqrt(2) is 16sqrt(2)pi^2