Posted by **Sophie** on Thursday, January 21, 2010 at 3:14am.

Which has more area, the region in the first quadrant enclosed by the line x+y=1 and the circle x^2+y^2=1, or the region in the first quadrant enclosed by the line x+y=1 and the curve sqrt(x)+sqrt(y)=1? Justify your answer.

- calculus -
**Reiny**, Thursday, January 21, 2010 at 9:24am
Nice Question!!!

The first one we can do without Calculus, it is simply the segment between the chord from (0,1) to (1,0), that is

pi/4 - 1/2 = (pi - 2)/4

the second equation is

√x + √y = 1

or

√y = 1-√x

y = (1-√x)^2 = 1 - 2√x + x for 0 <= x <= 1

the integral of 1 - 2√x + x is x - (4/3)x^(3/2) + (1/2)x^2

and the area enclosed by √x + √y = 1 , the x-axis, and the y-axis is (from 0 to 1)

(1 - 4/3 + 1/2) - 0

= 1/6

So the area between the curve √x + √y = 1 and the line x+y=1 is

1/2 - 1/6 = 1/3

then (pi-2)/4 = .2854

1/3 = .33333

So who is bigger?

## Answer this Question

## Related Questions

- Calculus AB...I really need help - The region in the first quadrant enclosed by ...
- calculus - Sketch the region in the first quadrant enclosed by the given curves...
- calculus - 1. Let R be the region in the first quadrant enclosed by the graphs ...
- calculus - Find the area of the region in the first quadrant enclosed by the ...
- calculus - Let R be the region in the first quadrant that is enclosed by the ...
- Calc AB - What is the area of the region in the first quadrant enclosed by the ...
- calculus - Find the volume of the solid generated by revolving the region about ...
- AP Calculus - Let R be the first quadrant region enclosed by the graph of y= 2e...
- calculus - A region is bounded in the second quadrant by the curve y = ln(1–x), ...
- math - The equations y=-2X+12, y=6-X, and X=0 enclose a region in quadrant I. ...

More Related Questions