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 16/3

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

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

\frac{16}{3}

Decimal Notation

5.33333 \dots

Solution steps

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

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

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

\int_{0}^{4} 2 d x = 8

= \frac{16}{3} - 8 + 8

Simplify

= \frac{16}{3}

x \to 1 lim (\frac{- 2}{x - 1})

\frac{d}{d x} (e^{x} + 2)

y = ln (5 x - 2)

x \to 1 lim (- \frac{2 x}{x - 1})

\int 6 e^{6 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 16/3