Answer
$\frac{124}{3}$
Work Step by Step
Recall: Let $f(x)\geq 0$ for $a\leq x\leq b$, the area under the graph of $y=f(x)$ and above the $x-$axis between $x=a$ and $x=b$ is represented by $A=\int_a^bf(x) dx$.
Using this knowledge to find the area in Question 47,
$Area=\int_0^4 (x^2+5)dx$
$=[\frac{x^3}{3}+5x]_0^4$
$=(\frac{4^3}{3}+5\cdot 4)-(\frac{0^3}{3}+5\cdot 0)$
$=(\frac{64}{3}+20)-(0+0)$
$=\frac{124}{3}$
Thus, the area is $\frac{124}{3}$.
