Question

If I have two equations- f(x)=0.02x^2-4x-4800 and g(x)=2x-2800 how do I find the area between these two functions?

Answer 1

Calculus 1?

Answer 2

I've been trying to write it as an definite integral, then antidifferentiate and solve by subbing the x values in. It just doesn't seem right.

Answer 3

Well, thats what you need to do, but first you need to figure out where they intersect. Obviously this is a line intersecting a parabola. Once you find the intersection points you'll know your interval of integration. Then determine which function is greater than the other. Test a value in the middle of the interval.

Answer 4

Did you find the intersection points?

Answer 5

Yes, the intersection points are (-200,-3200), (500,1800). I do not know how to determine which function is greater. I would assume it's the parabolic function.

Answer 6

Well, you can test at x = 0. This would be very easy.

Answer 7

Okay. That makes sense. It's just that the area I got before was like 11830.89 and I'm really not sure that's right because on the question there is a scale that states on the x axis ever unit is 10 meters and on the y axis 1 unit is a meter.

Answer 8

so it's all just stressing me out haha

Answer 9

What did you get for the integration then? As you know the area is the integration of, in this case, g(x) - f(x)

Answer 10

When I integrated the two functions I ended up with [0.02x-2x-2000] dx

Answer 11

[0.02x^2-2x-2000] dx I mean

Answer 12

rough sketch
using x=0, and what the graph of a line and a binomial would look like

Answer 13

You're going to be taking the integral of the difference of the upper function and lower function, so in this case the upper function is the linear one (g(x)), the lower one is the quadratic (f(x))

Answer 14

important points