# Calc

posted by .

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 = (y-1)² - 1, x = (y-1)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 -

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 -

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 x2-x1 = (y-1)^2 + 1 - ((x-1)^2 - 1) = 2

Area = ∫x dy from 0 to 2
= ∫ 2dy from 0 to 2
= [2y] from 0 to 2
= 4-0 = 4

check my thinking, seems too easy.

## Similar Questions

1. ### Calc

y = x^2 y = 6 - x Find the area of the region by integrating (a) with respect to x and (b) with respect to y.
2. ### Calc

y = x^2 y = 6 - x Find the area of the region by integrating (a) with respect to x and (b) with respect to y.
3. ### Calculus

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
4. ### Calc

Find the area of the region bounded by the curves y2 = x, y – 4 = x, y = –2, and y = 1. So far I have found that the area of the trapezoid which is 13.5. But for the other two areas I cannot find them. They could be: 27/2 22/3 …
5. ### calc

Find the number a such that the line x = a divides the region bounded by the curves x = y^2 − 1 and the y-axis into 2 regions with equal area. Give your answer correct to 3 decimal places.
6. ### calc

Find the area of the region bounded by the curves y equals the inverse sine of x divided by 4, y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative.
7. ### Calc

Find the number b such that the line y = b divides the region bounded by the curves y = 4x2 and y = 16 into two regions with equal area. (Round your answer to two decimal places.)