Question

What is the area (in square units) of the region under the curve of the function f(x)=x+3, on the interval from x=1 to x=3 ?

Answer 1

Answer:

10 square units

Step-by-step explanation:

We want to find the area under the curve $f(x)=x+3$ from x=1 to x=3.

We use definite integrals to find this area.

$\int\limits^3_1 {x+3} \, dx$

We integrate to obtain:

$\frac{x^2}{2}+3x|_1^3$

We evaluate the limits to get:

$\frac{3^2}{2}+3(3)-(\frac{1^2}{2}+3(1))$

$4.5+9-0.5-3=10$

Therefore the area under the curve from x=1 to x=3 is 10 square unit.