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

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

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

\int_{0}^{4} (x - \frac{x}{2}) d x

\frac{4}{3}

Solution steps

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

\int_{0}^{4} x d x = \frac{16}{3}

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

= \frac{16}{3} - 4

Simplify

\frac{16}{3} - 4 : \frac{4}{3}

= \frac{4}{3}

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

\int_{- 2}^{2} x 25 - x^{2} d x

\int_{0}^{4} (x + 2) d x

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

\int_{1}^{6} \frac{2 ln ( x )}{x} d x

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