What is the integral from 0 to 2 of pi((x-1)^2)^2 ?

The integral from 0 to 2 of pi((x-1)^2)^2 is (2pi)/5

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integral from 0 to 2 of pi((x-1)^2)^2

\int_{0}^{2} π ((x - 1)^{2})^{2} d x

\frac{2 π}{5}

Decimal Notation

1.25663 \dots

Solution steps

\int_{0}^{2} π ((x - 1)^{2})^{2} 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} ((x - 1)^{2})^{2} d x

Simplify

((x - 1)^{2})^{2} : (x - 1)^{4}

= π \cdot \int_{0}^{2} (x - 1)^{4} d x

Apply u-substitution

: \int_{- 1}^{1} u^{4} d u

= π \cdot \int_{- 1}^{1} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{- 1}^{1}

= π [\frac{u ^{5}}{5}]_{- 1}^{1}

Compute the boundaries:

\frac{2}{5}

= π \frac{2}{5}

Simplify

= \frac{2 π}{5}

y = b^{2} (a - x) 3

y^{^{''}} - 30 y^{^{'}} + 255 y = 0

\frac{d}{d x} ((2 x - x^{2})^{\frac{1}{2}})

\frac{\partial}{\partial x} (\frac{( x - y )}{( x + y )})

\frac{\partial}{\partial x} (e^{x + y + 3})

What is the integral from 0 to 2 of pi((x-1)^2)^2 ?
The integral from 0 to 2 of pi((x-1)^2)^2 is (2pi)/5