# Math Help - Find the area enclosed by the given curves

1. ## Find the area enclosed by the given curves

I need help in solving this..... Please and Thank You
And explain throughly for me please because i am 100% confused....
Find the area of the region in the first quadrant bounded by the line , the line , the curve , and the x-axis.

2. Solving the system formed by the two curves we find $x=\frac{1}{4}$

Then the area is

$A=\int_0^{\frac{1}{4}}8xdx+\int_{\frac{1}{4}}^1\fr ac{1}{\sqrt{x}}dx$

Can you continue?

3. no i can't.... i don't even know what you did.... lol

4. Originally Posted by red_dog
Solving the system formed by the two curves we find $x=\frac{1}{4}$

Then the area is

$A=\int_0^{\frac{1}{4}}8xdx+\int_{\frac{1}{4}}^1\fr ac{1}{\sqrt{x}}dx$

Can you continue?
Originally Posted by dizizviet
no i can't.... i don't even know what you did.... lol
The first thing you should do is draw the graph of the lines $y = 8x$ and $x = 1$ and the curve $y = \frac{1}{\sqrt{x}}$ and then shade the required region. Have you done that?

You need to find where the line and the curve intersect. Solve $8x = \frac{1}{\sqrt{x}}$ to get the x-coordinate.

The required region consists of two seperate parts. The part between the line and the x-axis, and the part between the curve and the x-axis. Find the area of each part.

There are several pre-calculus skills you need to have competency in. It might be wise to go back and revise those skills (finding where curves intersect, solving equations, drawing graphs etc.)

5. ok thanks alot you helped alot if i need help again i'll be sure to ask +)