Posted by Erica on Monday, October 10, 2011 at 2:27am.
Find the areas of the regions bounded by the lines and curves by expressing x as a function of y and integrating with respect to y.
x = (y1)²  1, x = (y1)² + 1 from y=0 to y=2.
I graphed the two functions and the do not intersect? Does it matter? Or do I still find the area in between?
Thank you!

Calc  MathMate, Monday, October 10, 2011 at 8:56am
You're right, unless you have made a typo, the two curves will never intersect.
As you said, it does not matter, the lines y=0 and y=2 will intersect both lines to make a curved rectangle whose area you'd have to calculate. The result should be a nice integer.

Calc  Reiny, Monday, October 10, 2011 at 8:59am
Even though they don't intersect, there is the area bounded between y=0 and y=2
Did you notice that the two parabolas are congruent and the second is merely translated 2 units to the right?
so the horizontal distance between corresponding points is always 2
that is x2x1 = (y1)^2 + 1  ((x1)^2  1) = 2
Area = ∫x dy from 0 to 2
= ∫ 2dy from 0 to 2
= [2y] from 0 to 2
= 40 = 4
check my thinking, seems too easy.
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