What is the integral from 0 to 3 of 2sqrt(x+1)-2 ?

The integral from 0 to 3 of 2sqrt(x+1)-2 is 10/3

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integral from 0 to 3 of 2sqrt(x+1)-2

\int_{0}^{3} 2 x + 1 - 2 d x

\frac{10}{3}

Decimal

3.33333 \dots

Solution steps

\int_{0}^{3} 2 x + 1 - 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

= \int_{0}^{3} 2 x + 1 d x - \int_{0}^{3} 2 d x

\int_{0}^{3} 2 x + 1 d x = \frac{28}{3}

\int_{0}^{3} 2 d x = 6

= \frac{28}{3} - 6

Simplify

\frac{28}{3} - 6 : \frac{10}{3}

= \frac{10}{3}

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What is the integral from 0 to 3 of 2sqrt(x+1)-2 ?
The integral from 0 to 3 of 2sqrt(x+1)-2 is 10/3