What is the integral from 1 to 6 of pi(x-1) ?

The integral from 1 to 6 of pi(x-1) is pi 25/2

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integral from 1 to 6 of pi(x-1)

\int_{1}^{6} π (x - 1) d x

π \frac{25}{2}

Decimal Notation

39.26990 \dots

Solution steps

\int_{1}^{6} 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}^{6} 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}^{6} x d x - \int_{1}^{6} 1 d x)

\int_{1}^{6} x d x = \frac{35}{2}

\int_{1}^{6} 1 d x = 5

= π (\frac{35}{2} - 5)

Join

\frac{35}{2} - 5 : \frac{25}{2}

= π \frac{25}{2}

\frac{d r}{d t} = 6 (t + 1)^{\frac{1}{2}}, r (0) = 0

(3.6) (5.1)

f (x) = 2 e^{x}

2 x^{3} - x^{2} + 2 (1.3)

\int \frac{2 x ^{2} + x - 4}{x ^{3} - x ^{2} - 2 x} d x

What is the integral from 1 to 6 of pi(x-1) ?
The integral from 1 to 6 of pi(x-1) is pi 25/2