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

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

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

\int_{0}^{2} π (x + 1)^{2} d x

π \frac{26}{3}

Decimal Notation

27.22713 \dots

Solution steps

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

Expand

(x + 1)^{2} : x^{2} + 2 x + 1

= 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}

\frac{d}{d x} (x^{4} + 3 x)

\int \frac{lo g _{3} ( x )}{x} d x

y^{^{'}} + (\frac{1 + x}{x}) y = 0

y = ln (x^{2}), (5, ln (25))

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