Question

I have been working on this forever i cant seem to find the intervals! find the area of the region

2 y = 4 \sqrt{x},y = 5, 2 y + 2 x = 6

Answer 1

first solve each one for y

y=5
y = 2/sqrt(x)
y = 3-x

3-x = 5
--> x = -2

2/sqrt(x) = 5
--> x = 4/25

3-x = 2/sqrt(x)
look at graph, notice they intersect close to 1
check
3-1 = 2/1
2=2
--> x=1

\[A = \int\limits_{-2}^{4/25}5-(3-x) dx + \int\limits_{4/25}^{1}\frac{2}{\sqrt{x}}-(3-
x)dx\]