How to find the area under multiple curves

Question

I have a problem here that involves three equations. It wants to know the total area that is bounded by these three equations. they are as follows:

y=x

y=7

y=x²/28

The domain is [0,14]

I know I'm going to use some sort of integral, but I'm not sure how to work in all three equations. I would deeply appreciate some help!! 

Answer 1

Hi Noelle,

 

Yes you do have to use some integral. But the problem is more of a test of your on graphs than calculus. 

 

Once you are able to graph it and shade the area of interest it will be straightforward evaluation of integrals.

 

Your graph is bounded by y=7 from the top, y=x from the left and y=x^2/28 from the left.

 

Divide your shaded area vertically in to two regions at x=7

 

Find the area on the left by integrating the square function and subtracting it from the area of the triangle

 

Find the area under the square function and subtract it from the area of the square (on second taught you may not have to break up the area. You can just integrate the sqr w/t 0 and 14 as the upper limit and subtract that from the sum of the square and the triangle)

 

I hope this helps