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

The integral from 0 to 4 of 2sqrt(x)-x is 8/3

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

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

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

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

\int_{0}^{4} 2 x d x = \frac{32}{3}

\int_{0}^{4} x d x = 8

= \frac{32}{3} - 8

Simplify

\frac{32}{3} - 8 : \frac{8}{3}

= \frac{8}{3}

x \to 0 lim (\frac{1}{x ^{3} - 1} + 1)

x \to 0 lim (\frac{x ^{2} - 5}{x})

t \to - 2 lim (t^{2} + 5 t + 7)

\int tan^{3} (\frac{x}{2}) sec^{3} (\frac{x}{2}) d x

f^{^{'}} (x) = \frac{2 x ^{2} - 9 x + 8}{6 x + 5}

What is the integral from 0 to 4 of 2sqrt(x)-x ?
The integral from 0 to 4 of 2sqrt(x)-x is 8/3