I have seen the problem completed online and it was answered for me here too, bu
ID: 3117876 • Letter: I
Question
I have seen the problem completed online and it was answered for me here too, but the person didn't answer my follow up question. The online solution I saw somewhere else claimed it was 8/3 with the range from -2 to 2. The person who answered mine on chegg, claimed it was 8/3, but did a range from -1 to 1 ... so they used the points of intersection and clipped off the area between -2 to -1 and 1 to 2. I found the points of intersection, then did the definite integral from -2 to 1 and then the definite integral from -1 to 0 ... I then multiplied by 2 to get the area of the entire thing. Is the answer 8/3 or are these other people leaving out the area from -2 to -1 and 1 to 2. I just don't see what I'm doing wrong ... can't just whack out the areas past the points of intersection can you? Thanks
Explanation / Answer
y= x^2+1
y=3-x^2
y=y intersection points
x^2+1 = 3-x^2
2 x^2 = 2
x^2 = 1
x= -1
x= +1
we need area from x=-2 to x= 2
Area = int_{x=-2]^{-1} ( x^2 +1 - (3-x^2) ) dx + int_{x=-1]^{1} (3-x^2 -(x^2+1)) dx
+ int_{x=1]^{2} ( x^2 +1 - (3-x^2) ) dx
Area = 8/3 + 8/3 + 8/3 = 24 / 3 = 8 ANSWER