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

The integral from 0 to 16 of sqrt(x)-4 is -64/3

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

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

- \frac{64}{3}

Decimal Notation

- 21.33333 \dots

Solution steps

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

\int_{0}^{16} x d x = \frac{128}{3}

\int_{0}^{16} 4 d x = 64

= \frac{128}{3} - 64

Simplify

\frac{128}{3} - 64 : - \frac{64}{3}

= - \frac{64}{3}

y^{^{''}} + 2 y^{^{'}} + 10 y = 0, y (0) = 4, y^{^{'}} (0) = - 2

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

x^{5} + y^{4} x^{6} + 5 y^{^{'}} = 0, y (0) = 0

\int sec (2 x) d x

y = 2 x^{3} - 2 x

What is the integral from 0 to 16 of sqrt(x)-4 ?
The integral from 0 to 16 of sqrt(x)-4 is -64/3