How to find area under the curve?

Question

-25000 x^2 + 10,000 x + 15,000

Is this a parabola?

Answer 1

Yes, this is the equation of a parabola which opens downward. This equation can be factored into:

(-250 x - 150)(100 x - 100)

Set it equal to zero, and find the roots of the equation:

-25000 x^2 + 10,000 x + 15,000 = 0.

Using the factors above, we can find which values of x make each factor equal to 0, and thus the whole equation equal to 0.

-250 x - 150 = 0 ---> x = 150/-250 = -3/5

100 x - 100 = 0 ---> x = 100/100 = 1

Now, to find the area under the curve, use the above two values for your limits of integration and integrate term by term to get this:

(-25000 x^3) / 3 + (10000 x^2) / 2 + 15000 x = (-25000 x^3) / 3 + 5000 x^2 + 15000 x.

The area under the curve is the functional value of the upper limit, x = 1, minus the functional value of the lower limit, x = -3 /5.

-25000 (1^3) / 3 + 10000 (1^2) / 2 + 15000 (1) =
-25000 (1^3) / 3 + 5000 (1^2) + 15000 (1) =
25000 (1^3) / 3 + [(20000) (3)] / 3 =
(60000 - 25000) / 3 =
35000 / 3.

Now, let x = -3/5.

[-25000 (-3/5)^3] / 3 + [10000 (-3/5)^2] / 2 + [15000 (-3/5)] =
[-25000 (-27/325)] + [(10000(9/50)] - (45000 / 5) =
(675000 / 375) + (90000 / 25) - 9000 =
1800 + 1800 - 9000 =
-5400.

If we convert it to thirds, we get: -16200 / 3.

Now, to find the area under the curve, we subtract the second result from the first:

(35000 / 3) - (-16200 / 3) =
(35000 / 3) + (16200 / 3) =
51200 / 3 square units.

Answer 2

Yes it is an upsidedown parabola. I assume that you want the area between the x-axis (y=0) and the parabola. So you will need to integrate your equation and find the 2 x intercepts for the parabola and then solve the integral with those two values.

Answer 3

The equation is in the form nx^2+mx+b, which describes a parabolic form. It's not complete, however: you must specify what the equation equals, which is probably zero.

Integral calculus will tell you the area beneath the equation and above the x-axis between any two given points; it will also supply the equation of that area so it can be calculated at any time.

Answer 4

Yeah, its a quadratic formula, and its shape is a parabola.

What's the curve for the area problem??

Answer 5

yea what he said

Answer 6

integrate it