Find the area enclosed by the given curves

• Apr 12th 2009, 10:38 AM
dizizviet
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.... (Headbang)
Find the area of the region in the first quadrant bounded by the line http://image.cramster.com/answer-boa...9675002601.gif, the line http://image.cramster.com/answer-boa...8737502068.gif, the curve http://image.cramster.com/answer-boa...9987508061.gif, and the x-axis.
• Apr 12th 2009, 11:25 AM
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?
• Apr 12th 2009, 05:12 PM
dizizviet
no i can't.... (Crying) i don't even know what you did.... lol
• Apr 12th 2009, 05:32 PM
mr fantastic
Quote:

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?

Quote:

Originally Posted by dizizviet
no i can't.... (Crying) 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.)
• May 11th 2009, 03:56 PM
dizizviet
ok thanks alot you helped alot if i need help again i'll be sure to ask +)