What is the integral from 2 to 3 of pi(x+x^2)^2 ?

The integral from 2 to 3 of pi(x+x^2)^2 is pi 2431/30

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integral from 2 to 3 of pi(x+x^2)^2

\int_{2}^{3} π (x + x^{2})^{2} d x

π \frac{2431}{30}

Decimal Notation

254.57372 \dots

Solution steps

\int_{2}^{3} π (x + x^{2})^{2} d x

Take the constant out:

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

= π \cdot \int_{2}^{3} (x + x^{2})^{2} d x

Expand

(x + x^{2})^{2} : x^{2} + 2 x^{3} + x^{4}

= π \cdot \int_{2}^{3} x^{2} + 2 x^{3} + x^{4} 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_{2}^{3} x^{2} d x + \int_{2}^{3} 2 x^{3} d x + \int_{2}^{3} x^{4} d x)

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 2 x^{3} d x = \frac{65}{2}

\int_{2}^{3} x^{4} d x = \frac{211}{5}

= π (\frac{19}{3} + \frac{65}{2} + \frac{211}{5})

Join

\frac{19}{3} + \frac{65}{2} + \frac{211}{5} : \frac{2431}{30}

= π \frac{2431}{30}

f (x) = \frac{11}{2} - x^{2}, at x = - 2

\int cos (2 x - 3) d x

k = 0 \sum \infty (\frac{1}{2})^{2 k + 1}

\frac{x ( x - 1 ) ( x - 2 ) ( x - 3 )}{24}

\frac{\partial}{\partial x} (e^{2 x} - 2 y)

What is the integral from 2 to 3 of pi(x+x^2)^2 ?
The integral from 2 to 3 of pi(x+x^2)^2 is pi 2431/30