What is the integral from 2 to 6 of pi(y-2)2 ?

The integral from 2 to 6 of pi(y-2)2 is 16pi

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integral from 2 to 6 of pi(y-2)2

\int_{2}^{6} π (y - 2) 2 d y

16 π

Decimal Notation

50.26548 \dots

Solution steps

\int_{2}^{6} π (y - 2) \cdot 2 d y

Take the constant out:

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

= π 2 \cdot \int_{2}^{6} y - 2 d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= π 2 (\int_{2}^{6} y d y - \int_{2}^{6} 2 d y)

\int_{2}^{6} y d y = 16

\int_{2}^{6} 2 d y = 8

= π 2 (16 - 8)

Simplify

= 16 π

f (x) = 5 x, at x = 16

y^{^{''}} + 2 y^{^{'}} + y = 2 e^{- t}

\frac{x + 2}{x - 1}

\frac{d y}{d x} = \frac{cos ( 5 x )}{e ^{5 y}}

\int \frac{2 e ^{2 x}}{1 + e ^{2 x}} d x

What is the integral from 2 to 6 of pi(y-2)2 ?
The integral from 2 to 6 of pi(y-2)2 is 16pi