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

The integral from 0 to 16 of 4sqrt(x)-x is 128/3

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integral from 0 to 16 of 4sqrt(x)-x

\int_{0}^{16} 4 x - x d x

\frac{128}{3}

Decimal Notation

42.66666 \dots

Solution steps

\int_{0}^{16} 4 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}^{16} 4 x d x - \int_{0}^{16} x d x

\int_{0}^{16} 4 x d x = \frac{512}{3}

\int_{0}^{16} x d x = 128

= \frac{512}{3} - 128

Simplify

\frac{512}{3} - 128 : \frac{128}{3}

= \frac{128}{3}

\frac{\partial}{\partial y} (\frac{8.31 x}{y})

x^{^{'}} = x^{2}

e^{2 t} cos (3 t + 5)

\frac{1}{4 + x}

z \to 0 lim (\frac{8}{z ^{3}} + \frac{5}{z} + 2)

What is the integral from 0 to 16 of 4sqrt(x)-x ?
The integral from 0 to 16 of 4sqrt(x)-x is 128/3