What is the integral from 0 to 60 of (60-y)^2 ?

The integral from 0 to 60 of (60-y)^2 is 72000

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integral from 0 to 60 of (60-y)^2

\int_{0}^{60} (60 - y)^{2} d y

72000

Solution steps

\int_{0}^{60} (60 - y)^{2} d y

Expand

(60 - y)^{2} : 3600 - 120 y + y^{2}

= \int_{0}^{60} 3600 - 120 y + 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

= \int_{0}^{60} 3600 d y - \int_{0}^{60} 120 y d y + \int_{0}^{60} y^{2} d y

\int_{0}^{60} 3600 d y = 216000

\int_{0}^{60} 120 y d y = 216000

\int_{0}^{60} y^{2} d y = 72000

= 216000 - 216000 + 72000

Simplify

= 72000

x y^{^{'}} + y = 3 x y

\int_{1}^{10} \frac{1}{x ^{2}} d x

x^{2} (sin (x))

\frac{d y}{d x} = y \cdot (\frac{1}{x} - y)

\frac{\partial}{\partial u} (\frac{v}{u})

What is the integral from 0 to 60 of (60-y)^2 ?
The integral from 0 to 60 of (60-y)^2 is 72000