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

The integral from 0 to 4 of 4sqrt(x)-2x is 16/3

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

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

\frac{16}{3}

Decimal Notation

5.33333 \dots

Solution steps

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

\int_{0}^{4} 4 x d x = \frac{64}{3}

\int_{0}^{4} 2 x d x = 16

= \frac{64}{3} - 16

Simplify

\frac{64}{3} - 16 : \frac{16}{3}

= \frac{16}{3}

\frac{d y}{d x} = e^{3 x} + 9 y

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

\int_{2}^{3} \frac{22}{3 - x} d x

f (x) = x^{3} - 4 x, at x = 0

\frac{2}{( s + 2 )}

What is the integral from 0 to 4 of 4sqrt(x)-2x ?
The integral from 0 to 4 of 4sqrt(x)-2x is 16/3