What is the integral from 0 to t of 1000x+250 ?

The integral from 0 to t of 1000x+250 is 250t+500t^2

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integral from 0 to t of 1000x+250

\int_{0}^{t} 1000 x + 250 d x

250 t + 500 t^{2}

Solution steps

\int_{0}^{t} 1000 x + 250 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

= \int_{0}^{t} 250 d x + \int_{0}^{t} 1000 x d x

\int_{0}^{t} 250 d x = 250 t

\int_{0}^{t} 1000 x d x = 500 t^{2}

= 250 t + 500 t^{2}

What is the integral from 0 to t of 1000x+250 ?
The integral from 0 to t of 1000x+250 is 250t+500t^2