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

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

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

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

- \frac{19}{6}

Decimal Notation

- 3.16666 \dots

Solution steps

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

Simplify

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

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

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

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

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

Simplify

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

= - \frac{19}{6}

\int_{0}^{h} \frac{b}{h} (h - y) d y

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

\int_{0}^{π} cos (\frac{1}{2}) x d x

x \to \frac{π}{2} lim (\frac{cos ( x )}{1 - sin ( x )})

x \to \frac{π}{2} lim (\frac{ln ( sin ( x ) )}{( π - 2 x ) ^{2}})

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