What is the integral from 0 to 4 of pi(sqrt(x-1))^2 ?

The integral from 0 to 4 of pi(sqrt(x-1))^2 is 4pi

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integral from 0 to 4 of pi(sqrt(x-1))^2

\int_{0}^{4} π (x - 1)^{2} d x

4 π

Decimal Notation

12.56637 \dots

Solution steps

\int_{0}^{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_{0}^{4} (x - 1)^{2} d x

Simplify

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

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

\int_{0}^{4} x d x = 8

\int_{0}^{4} 1 d x = 4

= π (8 - 4)

Simplify

= 4 π

x \to - 5 lim (\frac{2}{( x + 5 ) ^{4}})

\int 1024 sin^{4} (x) cos^{4} (x) d x

\int \frac{t ^{5}}{( t ^{3} + 1 ) ^{2}} d t

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

y = x 3600 - x^{2}

What is the integral from 0 to 4 of pi(sqrt(x-1))^2 ?
The integral from 0 to 4 of pi(sqrt(x-1))^2 is 4pi