How do I find the area between two functions? One is a parabola, the other linear.

Question

anonymous · Answer

attachment

lgbasallote · Answer

do you know calculus?

anonymous · Answer

Still in the process of learning it but I don't have a strong knowledge.

lgbasallote · Answer

first...you need to know which area you're looking for

anonymous · Answer

I know I'm looking for the area that is enclosed by the linear function.

lgbasallote · Answer

well that's a good first step...next is you need to identify the equation of the curve and the line

anonymous · Answer

I already have haha or I wouldn't have been able to draw them. The parabola is y=0.02x^2-2x-4800 and the linear equation is y=2x-2800

lgbasallote · Answer

good...now identify...which one is on the top...the line? or the graph?

ghazi · Answer

|dw:1345973267188:dw| use double integration to find the area enclosed your function will be $$\int\limits_{-x}^{x}\int\limits_{x^2}^{x} dxdy$$

anonymous · Answer

the linear equation is the one on top?

lgbasallote · Answer

right

ghazi · Answer

limit of dx is from the equation of parabola in terms of x to the linear equation and limit of y is from left of x to the right ...that is the two points where line cuts parabola

lgbasallote · Answer

now use the formula $$\Large \int \limits_{x=a}^{x=b} [f(x) - g(x)]dx$$
do you know that thingy?

anonymous · Answer

yeaahhh I have used that. where b and a are the upper and lower intersects?

lgbasallote · Answer

b and a are the left and right limits

anonymous · Answer

okay.

lgbasallote · Answer

wait.. a is left limit; b is right limit

lgbasallote · Answer

so what would your limits be>

anonymous · Answer

um, so it should end up looking something like $$\int\limits_{-200}^{-500}[(0.02x ^{2}-4x-4800-(-2x-2800)]$$

lgbasallote · Answer

nope...remember you said the linear equation was on top the curve?

anonymous · Answer

yeah?

anonymous · Answer

it crosses through the parabola at (-200,3200) and (-500,-1800)

lgbasallote · Answer

the top function is always the minuend

lgbasallote · Answer

$$\int (top - bottom)dx$$
got it?

anonymous · Answer

Ohhh okay. So.. $$\int\limits_{-500}^{-200}[-2x-2800]-[0.02x^2-4x-4800)]$$

anonymous · Answer

dx at the end as well >.<

lgbasallote · Answer

right

anonymous · Answer

then can I just plug that into my calculator and get a result from there?

lgbasallote · Answer

yup. and according to mine..this is big

anonymous · Answer

I got -390000

lgbasallote · Answer

http://www.wolframalpha.com/input/?i=int_-500%5E-200+%28-2x+-+2800+-+0.02x%5E2%2B+4x+%2B+4800%29dx

anonymous · Answer

yep, same as my result. :)