What is the integral from 0 to 2 of pi(2-x) ?

The integral from 0 to 2 of pi(2-x) is 2pi

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integral from 0 to 2 of pi(2-x)

\int_{0}^{2} π (2 - x) d x

2 π

Decimal

6.28318 \dots

Solution steps

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

\int_{0}^{2} 2 d x = 4

\int_{0}^{2} x d x = 2

= π (4 - 2)

Simplify

= 2 π

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What is the integral from 0 to 2 of pi(2-x) ?
The integral from 0 to 2 of pi(2-x) is 2pi