## Question:

Determine the equivalent resultant force of the distributed loading and its location, measured from point $A$. Evaluate the integrals using Simpson’s rule.

Units Used:

$kN$ = ${ 10 }^{ 3 }$ $N$

Given:

${ c }_{ 1 }$ = $5$

${ c }_{ 2 }$ = $16$

$a$ = $3$

$b$ = $1$

## Step-by-step

${ F }_{ R }$ = $\int _{ 0 }^{ a+b }{ \sqrt { { c }_{ 1 }x\sqrt { { c }_{ 2 }+{ x }^{ 2 } } } dx } \quad \quad \quad \quad { F }_{ R }$ = $14.9$

$d$ = $\frac { \int _{ 0 }^{ a+b }{ x\sqrt { { c }_{ 1 }x\sqrt { { c }_{ 2 }+{ x }^{ 2 } } } dx } }{ { F }_{ R } } \quad \quad\quad\quad\quad\quad \quad d$ = $2.27$