SOLUTION: What is the approximate area of the region bounded by the graphs: y equals one-half times x squared plus 2., x = 0 , x = 3 and y = 0 (the yellow region)? Show all work to receiv

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Question 111411: What is the approximate area of the region bounded by the graphs:
y equals one-half times x squared plus 2., x = 0 , x = 3 and y = 0 (the yellow region)?
Show all work to receive credit.
The graph of y equals one-half times x squared plus 2 is drawn. The area under the graph and bounded by the lines y equals 0, x equals zero and x equals 3 is shaded yellow.
I know this sounds confusing, I couldn't figure out how to draw it. On the graph
it looks like a parabala the yellow region is on the positive side of the x axis beneath the parabala. It is divided into 3 sections. (1,0)(2,0)and(3,0)
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Find the approximate area of the region bounded by , , , and
First, it would be helpful to see the graph of the equation:

Now divide the region into two areas by a vertical line through x = 2 and another vertical line through x = 3.
You can approximate the shape of these two area by trapezoids (lying on their sides).
The first trapezoid and
How did I get these?
Just substitute x = 0 into the equation and solve for y.

and...

Now you can find the area of the first trapezoid using:
The h here is just x = 2, so...

For the second trapezoid, you have: and from:

and...

So, the area of the second trapezoid is:

Finally, add these two areas together to get:

as the approximate area of the enclosed region.