Evaluate the integral (3 - 2x)dx for x = -1 to x = 3
byinterpreting it in terms of areas.

4 unit^2

explanation is given at the end.

Step-by-step explanation:

What this integral represents is the net area between the function f(x) = 3 - 2x

and the x-axis, between the range of x between -1 and 3.

we have integrated the equation, and now we're going to put the limits find the area under the function f(x)

-------------

if these seems like a big jump, try to understand it through this:

we've only distributed the limits each time to the same integrated expression.

--------------

coming back to our solution:

so our area is 4

the area above the x-axis is positive, and the area below the x-axis is negative. Since, our answer is +4. We now know that if within this range [-1,3] the area above and below the x-axis exist, there is more area above the x-axis than below the x-axis. In other words, the net area is above the x-axis and that is equal to 4 unit^2

domain is all the x values included in the

0 ≤ x ≤ 2

range is all the y values of the graph

-2 ≤ y ≤ 2

***keep in mind that there are different ways to show domain and range

hope this !

~just a girl in love with shawn mendes