# Thread: Area Enlcosed By Curves

1. ## Area Enlcosed By Curves

Find the area of the region enclosed by the curves:

2y=4*sqrtx, y = 4, 2y + 3x = 7

I'm having a little difficulty with this problem. Is the upper bound function y=4?

2. Yes, the upper bound function is $y=4$.

I suggest you to do a graph of the situation to follow my answer.

First, we'll find the intersection between $2y+3x=7$ and $y=4$. Just replacing, we obtain $8+3x=7\Rightarrow x=-\frac{1}{3}$, $\therefore$ the functions intersects at $\left(-\frac{1}{3},4\right)$.

Doing the same, we conclude that $2y+3x=7$ and $y=2\sqrt{x}$ insersects at $\left(1,2\right)$.

Finally, the area is given by $\int_{-\frac{1}{3}}^14-\left(-\frac{3}{2}x+\frac{7}{2}\right)dx+\int_1^44-2\sqrt{x}dx$.