What is the integral from 0 to 4 of (1-sqrt(x)) ?

The integral from 0 to 4 of (1-sqrt(x)) is -4/3

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integral from 0 to 4 of (1-sqrt(x))

\int_{0}^{4} (1 - x) d x

- \frac{4}{3}

Decimal Notation

- 1.33333 \dots

Solution steps

\int_{0}^{4} 1 - 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} 1 d x - \int_{0}^{4} x d x

\int_{0}^{4} 1 d x = 4

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

= 4 - \frac{16}{3}

Simplify

4 - \frac{16}{3} : - \frac{4}{3}

= - \frac{4}{3}

\int_{- 1}^{1} 1 - x d x

\int_{- 1}^{1} (x^{4} - x^{5}) d x

\int_{0}^{\frac{π}{2}} sec^{4} (\frac{x}{2}) d x

\int_{- 4}^{4} x^{2} - 16 d x

\int_{0}^{1} \frac{1}{3 x - 2} d x

What is the integral from 0 to 4 of (1-sqrt(x)) ?
The integral from 0 to 4 of (1-sqrt(x)) is -4/3