Definite Integral/Examples/Root x from 0 to 4

Example of Definite Integral

$\ds \int_0^4 \sqrt x \rd x = \dfrac {16} 3$

Proof

\(\ds \int_0^4 \sqrt x \rd x\)

\(=\)

\(\ds \intlimits {\dfrac {2 x^{3/2} } 3} 0 4\)

Primitive of Square Root

\(\ds \)

\(=\)

\(\ds \dfrac {2 \times \sqrt 4^3} 3 - \dfrac {2 \times \sqrt 0^3} 3\)

Definition of Definite Integral

\(\ds \)

\(=\)

\(\ds \dfrac {16} 3\)

evaluating

$\blacksquare$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Exercises $\text {XV}$: $1. \ \text{(b)}$