Answer
$2$
Work Step by Step
Step 1. Graph the function for the given interval of $0\leq x\leq 4$ and identify a zero at $x=1$, which separates the positive and negative regions.
Step 2. The total area is the sum of the absolute value of the two separate areas $A_1$ and $A_2$.
Step 3. Evaluate
$A_1=\int_0^1(1-\sqrt x)dx=(x-\frac{2}{3}x^{3/2})|_0^1=1-\frac{2}{3}=\frac{1}{3}$
Step 4. Evaluate
$A_2=\int_1^4(1-\sqrt x)dx=(x-\frac{2}{3}x^{3/2})|_1^4=(4-\frac{2}{3}(4)^{3/2})-(1-\frac{2}{3})=-\frac{5}{3}$
Step 5. Thus, we have the area as $A=|A_1|+|A_2|=2$
