Question

Use limits to find the area between the curve of y = x and the x-axis for the interval from
x= 1 to x= 3.
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Answer 1

Answer:

The area between the curves is 4 square units.

Step-by-step explanation:

We want to find the area bounded by:

y = x

x = 0

in the interval x = 1, x = 3

This is simply equal to the integral of the function f(x) = x between x = 1 and x = 3

Written as:

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

And the integral of x is equal to x^2/2

Then:

$\int\limits^3_1 {x} \, dx = (\frac{3^2}{2} - \frac{1^2}{2}) = (\frac{9}{2} - \frac{1}{2} ) = \frac{8}{2} = 4$

The area between the curves is 4 square units.