Find the formula for the area of the shaded region in the figure.

Question

konradzuse · Answer

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kainui · Answer

Are you allowed to use calculus?

kainui · Answer

Consider that h is the y-value of the function at x, so you can plug in h for y to solve for x. From there you'll have the information you need to find the area of the rectangle, but you want to subtract out the area under the parabola, so set up an integral from 0 to x and multiply the answer by 2 since the area under the whole curve is the same as 2 times the area from 0 to x. Make sense or too confusing? I can clarify anything.

konradzuse · Answer

Yeah I'm in Calc 2.

konradzuse · Answer

I'm rereading the chapter, the professor's notes are horrid, they just give examples, no explanation provided....

kainui · Answer

Sure, so do you understand what an integral does? I can help with this problem, I know the answer.

konradzuse · Answer

Yeah, this is the last chapter of the course, there were a few forms that were in her notes, but like I said they were poor.

konradzuse · Answer

Okay I just read your paragraph, missed it before...  How exactly do we set up this integral?  

You said from 0 to x?  $$\int\limits_{0}^{x}$$??

kainui · Answer

Well you want to find out the area of this rectangle looking piece minus the area under the parabola, right? |dw:1344114975291:dw| 

So you can either integrate from -x to x, or you can integrate from 0 to x and multiply it by 2, it's exactly the same answer, I might have just complicated it by multiplying it by 2.