Let R be the region bounded by the x-axis, the graph y=(x+1)^(1/2), and the line x=3. Find the value h such that the vertical line x=h divides the region R into 2 regions of equal area.

Question

anonymous · Answer

how far have you reached? i will help you further

tkhunny · Answer

What's your plan.  There should be some integrals in your future.

anonymous · Answer

I have already calculated that the area is 5.3333. So assumed that I should divide that by 2 and work backwards form there?

tkhunny · Answer

Backwards?  No.  Solve for a  $\int\limits_{-1}^{a}\sqrt{x+1}\;dx = \dfrac{8}{3}$

anonymous · Answer

WHere did the 8/3 come from?

tkhunny · Answer

The problem statement, "divides the region R into 2 regions of equal area. "

The area of the region is 16/3.  Half the area is 8/3.

Note: I guess I should have used 'h' instead of 'a'.  The name is given in the problem statement.

anonymous · Answer

So would i integrate and place h in the place of x and subtract f(-1)?

anonymous · Answer

I did this wrong... i got 7

tkhunny · Answer

Just like you already did when you found the total area.

You could also do it the other way, [h,3], instead of [-1,h].

tkhunny · Answer

Good call.  h = 7 clearly is no good.

anonymous · Answer

Can you slowly go step by step on this. I'm just not use to seeing a letter on the integral

tkhunny · Answer

How did you get the total area?

anonymous · Answer

the integral of (x+1)^(1/2) form -1 to 3

tkhunny · Answer

Please demonstrate this.  How did you find the correct value of that integral?