What is the integral from 0 to 2 of pi(x^2+2x+1) ?

The integral from 0 to 2 of pi(x^2+2x+1) is pi 26/3

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integral from 0 to 2 of pi(x^2+2x+1)

\int_{0}^{2} π (x^{2} + 2 x + 1) d x

π \frac{26}{3}

Decimal

27.22713 \dots

Solution steps

\int_{0}^{2} π (x^{2} + 2 x + 1) d x

Take the constant out:

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

= π \cdot \int_{0}^{2} x^{2} + 2 x + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π (\int_{0}^{2} x^{2} d x + \int_{0}^{2} 2 x d x + \int_{0}^{2} 1 d x)

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 2 x d x = 4

\int_{0}^{2} 1 d x = 2

= π (\frac{8}{3} + 4 + 2)

Simplify

π (\frac{8}{3} + 4 + 2) : π \frac{26}{3}

= π \frac{26}{3}

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What is the integral from 0 to 2 of pi(x^2+2x+1) ?
The integral from 0 to 2 of pi(x^2+2x+1) is pi 26/3