Answer :
Answer:
11.968 square units.
Step-by-step explanation:
The given equation of the curve is
[tex]y=2+\sqrt{x}[/tex]
We need to write the summation to estimate the area under the given curve from x=2 to x=5 using 3 rectangles and right endpoints.
End points are : 2,3,4,5
Right end points are : 3,4,5
Find the value of the function at x=3,4,5.
At x=3,
[tex]y=2+\sqrt{3}[/tex]
At x=4,
[tex]y=2+\sqrt{4}=2+2=4[/tex]
At x=5,
[tex]y=2+\sqrt{5}[/tex]
The area of under the curve is
[tex]Area=\sum_{k=2}^5 \Delta xf(x_{k+1}})[/tex]
[tex]Area=1\cdot (2+\sqrt{3})+1\cdot (4)+1\cdot (2+\sqrt{5})[/tex]
[tex]Area=2+\sqrt{3}+4+2+\sqrt{5}[/tex]
[tex]Area=8+\sqrt{3}+\sqrt{5}[/tex]
[tex]Area\approx 11.968[/tex]
Therefore, the area under the curve 11.968 square units.
