What is the integral of pi((20sqrt(x))^2-(5x)^2) ?

The integral of pi((20sqrt(x))^2-(5x)^2) is pi(200x^2-(25x^3)/3)+C

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integral of pi((20sqrt(x))^2-(5x)^2)

\int π ((20 x)^{2} - (5 x)^{2}) d x

π (200 x^{2} - \frac{25 x ^{3}}{3}) + C

Solution steps

\int π ((20 x)^{2} - (5 x)^{2}) d x

Take the constant out:

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

= π \cdot \int (20 x)^{2} - (5 x)^{2} d x

Simplify

(20 x)^{2} - (5 x)^{2} : 400 x - 25 x^{2}

= π \cdot \int 400 x - 25 x^{2} 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 400 x d x - \int 25 x^{2} d x)

\int 400 x d x = 200 x^{2}

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

= π (200 x^{2} - \frac{25 x ^{3}}{3})

Add a constant to the solution

= π (200 x^{2} - \frac{25 x ^{3}}{3}) + C

\int \frac{t}{t ^{4} + 49} d t

y^{^{''}} - 2 y^{^{'}} - 3 y = - 3 x e^{- x}

\int \frac{x}{x - 5} d x

x \to 0 lim (x^{3} cos (\frac{1}{x}))

f (x) = (\frac{x x - 1}{2})

What is the integral of pi((20sqrt(x))^2-(5x)^2) ?
The integral of pi((20sqrt(x))^2-(5x)^2) is pi(200x^2-(25x^3)/3)+C