# Constructing Antiderivatives and areas

1. Jan 21, 2007

### Jacobpm64

1. The problem statement, all variables and given/known data
The origin and the point (a, a) are at opposite corners of a square. Calculate the ratio of the areas of the two parts into which the curve $$\sqrt{x} + \sqrt{y} = \sqrt{a}$$ divides the square.

2. Relevant equations
I'm sure there will be some use of A = bh. Perhaps maybe the pythagorean theorem if the square is cut exactly in half? I'm sure I'll be using a definite integral to find the areas.

3. The attempt at a solution
I have no clue where to go with this.

1. The problem statement, all variables and given/known data
In drilling an oil well, the total cost, C, consists of fixed costs (independent of the depth of the well) and marginal costs, which depend on depth; drilling becomes more expensive, per meter, deeper into the earth. Suppose the fixed costs are 1,000,000 riyals (the riyal is the unit of currency of Saudi Arabia), and the marginal costs are C'(x) = 4000 + 10x riyals/meter, where x is the depth in meters. Find the total cost of drilling a well x meters deep.

2. Relevant equations
I'm using I'll use a definite integral.

3. The attempt at a solution
Here's what I tried.
$$1,000,000 + \int (from 0 to x) of 4000 + 10x$$
Evaluating that:
$$1,000,000 + [4000 + 10x - (4000 + 10(0) ) ]$$
$$1,000,000 + [4000 + 10x - 4000]$$
$$1,000,000 + 10x$$ riyals is the total cost.

I need some direction on the first one.. And I would like confirmation on the second one.

2. Jan 21, 2007

### Mindscrape

For the first one, I would suggest drawing your two areas out.

For the second one, is a fixed cost supposed to mean a limit? In other words, does fixed cost mean that C(x)<=1,000,000? If, on the other hand, it means that there is some cost that automatically comes in when drilling even a millionth of a unit down then you did it right.