What is the integral from 1 to 4 of pi(sqrt(x-1))^2 ?

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

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integral from 1 to 4 of pi(sqrt(x-1))^2

\int_{1}^{4} π (x - 1)^{2} d x

π \frac{9}{2}

Decimal Notation

14.13716 \dots

Solution steps

\int_{1}^{4} π (x - 1)^{2} 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)^{2} d x

Simplify

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

= 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}

\frac{d y}{d x} = - \frac{6 x}{y}

\frac{200}{t + 2}

\int \frac{6000 - 2000 x}{( x ^{2} - 6 x + 10 ) ^{2}} d x

x^{2} y^{^{''}} - 4 x y^{^{'}} - 6 y = 0

\frac{5 e ^{x} x ^{\frac{3}{2}}}{2} + e^{x} x^{\frac{5}{2}}

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