What is the integral from 1 to 4 of pi(x-1) ?

The integral from 1 to 4 of pi(x-1) is pi 9/2

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integral from 1 to 4 of pi(x-1)

\int_{1}^{4} π (x - 1) d x

π \frac{9}{2}

Decimal

14.13716 \dots

Solution steps

\int_{1}^{4} π (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_{1}^{4} 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_{1}^{4} x d x - \int_{1}^{4} 1 d x)

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} 1 d x = 3

= π (\frac{15}{2} - 3)

Join

\frac{15}{2} - 3 : \frac{9}{2}

= π \frac{9}{2}

2 (2 - 3 x)^{2}

- 8 (x - 3)^{3} + 27

\int_{0}^{1} x^{k} d x

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

x \to 0 lim (- \frac{1}{x ^{4}})

What is the integral from 1 to 4 of pi(x-1) ?
The integral from 1 to 4 of pi(x-1) is pi 9/2