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

The integral from 0 to 4 of 2sqrt(x)-2x+4 is 32/3

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integral from 0 to 4 of 2sqrt(x)-2x+4

\int_{0}^{4} 2 x - 2 x + 4 d x

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

\int_{0}^{4} 2 x - 2 x + 4 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}^{4} 2 x d x - \int_{0}^{4} 2 x d x + \int_{0}^{4} 4 d x

\int_{0}^{4} 2 x d x = \frac{32}{3}

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 4 d x = 16

= \frac{32}{3} - 16 + 16

Simplify

= \frac{32}{3}

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What is the integral from 0 to 4 of 2sqrt(x)-2x+4 ?
The integral from 0 to 4 of 2sqrt(x)-2x+4 is 32/3