What is the integral from 1 to 4 of (2-x)-(-sqrt(x)) ?

The integral from 1 to 4 of (2-x)-(-sqrt(x)) is 19/6

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integral from 1 to 4 of (2-x)-(-sqrt(x))

\int_{1}^{4} (2 - x) - (- x) d x

\frac{19}{6}

Decimal

3.16666 \dots

Solution steps

\int_{1}^{4} 2 - x - (- x) d x

Simplify

= \int_{1}^{4} 2 - x + x 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}^{4} 2 d x - \int_{1}^{4} x d x + \int_{1}^{4} x d x

\int_{1}^{4} 2 d x = 6

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} x d x = \frac{14}{3}

= 6 - \frac{15}{2} + \frac{14}{3}

Simplify

6 - \frac{15}{2} + \frac{14}{3} : \frac{19}{6}

= \frac{19}{6}

What is the integral from 1 to 4 of (2-x)-(-sqrt(x)) ?
The integral from 1 to 4 of (2-x)-(-sqrt(x)) is 19/6