What is the integral from 2 to 3 of pi(4-1/2 x)^2 ?

The integral from 2 to 3 of pi(4-1/2 x)^2 is pi 91/12

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integral from 2 to 3 of pi(4-1/2 x)^2

\int_{2}^{3} π (4 - \frac{1}{2} x)^{2} d x

π \frac{91}{12}

Decimal

23.82374 \dots

Solution steps

\int_{2}^{3} π (4 - \frac{1}{2} x)^{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} (4 - \frac{1}{2} x)^{2} d x

Simplify

(4 - \frac{1}{2} x)^{2} : 16 - 4 x + \frac{1}{4} x^{2}

= π \cdot \int_{2}^{3} 16 - 4 x + \frac{1}{4} x^{2} 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} 16 d x - \int_{2}^{3} 4 x d x + \int_{2}^{3} \frac{1}{4} x^{2} d x)

\int_{2}^{3} 16 d x = 16

\int_{2}^{3} 4 x d x = 10

\int_{2}^{3} \frac{1}{4} x^{2} d x = \frac{19}{12}

= π (16 - 10 + \frac{19}{12})

Simplify

π (16 - 10 + \frac{19}{12}) : π \frac{91}{12}

= π \frac{91}{12}

\int - 4 x^{3} e^{- 2 x^{2}} d x

\frac{( s + 2 )}{s + 1}

(2 y + 2 t - 3) d t + (4 y + 2 t - 1) d y = 0

\frac{\partial}{\partial x} (7 e^{x^{10} y})

x \to 5 lim (x^{2} + 2 x - 3)

What is the integral from 2 to 3 of pi(4-1/2 x)^2 ?
The integral from 2 to 3 of pi(4-1/2 x)^2 is pi 91/12