What is the integral from 0 to 16 of 2sqrt(x)-x/2 ?

The integral from 0 to 16 of 2sqrt(x)-x/2 is 64/3

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integral from 0 to 16 of 2sqrt(x)-x/2

\int_{0}^{16} 2 x - \frac{x}{2} d x

\frac{64}{3}

Decimal Notation

21.33333 \dots

Solution steps

\int_{0}^{16} 2 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}^{16} 2 x d x - \int_{0}^{16} \frac{x}{2} d x

\int_{0}^{16} 2 x d x = \frac{256}{3}

\int_{0}^{16} \frac{x}{2} d x = 64

= \frac{256}{3} - 64

Simplify

\frac{256}{3} - 64 : \frac{64}{3}

= \frac{64}{3}

x \to - 1 lim (∣ x ∣)

y^{^{''}} - 4 y^{^{'}} + 13 y = 0

f (x) = \frac{2}{x ^{2} + 1}, ∣ x ∣

\int (x - 1)^{2} sin^{2} (x) d x

f (x) = \frac{9}{x ^{2}}, at x = 3

What is the integral from 0 to 16 of 2sqrt(x)-x/2 ?
The integral from 0 to 16 of 2sqrt(x)-x/2 is 64/3