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levacccp [35]
3 years ago
15

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 ?

Mathematics
1 answer:
aleksandrvk [35]3 years ago
8 0

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.

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