Answer:
10 square units
Step-by-step explanation:
We want to find the area under the curve [tex]f(x)=x+3[/tex] from x=1 to x=3.
We use definite integrals to find this area.
[tex]\int\limits^3_1 {x+3} \, dx[/tex]
We integrate to obtain:
[tex]\frac{x^2}{2}+3x|_1^3[/tex]
We evaluate the limits to get:
[tex]\frac{3^2}{2}+3(3)-(\frac{1^2}{2}+3(1))[/tex]
[tex]4.5+9-0.5-3=10[/tex]
Therefore the area under the curve from x=1 to x=3 is 10 square unit.
