What is the integral of (227-x)-(23+0.7x) ?

The integral of (227-x)-(23+0.7x) is -0.85x^2+204x+C

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integral of (227-x)-(23+0.7x)

\int (227 - x) - (23 + 0.7 x) d x

- 0.85 x^{2} + 204 x + C

Solution steps

\int 227 - x - (23 + 0.7 x) d x

Simplify

= \int - 1.7 x + 204 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 1.7 x d x + \int 204 d x

\int 1.7 x d x = 0.85 x^{2}

\int 204 d x = 204 x

= - 0.85 x^{2} + 204 x

Add a constant to the solution

= - 0.85 x^{2} + 204 x + C

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What is the integral of (227-x)-(23+0.7x) ?
The integral of (227-x)-(23+0.7x) is -0.85x^2+204x+C