Question

What is this asking: Graph f(x) = cosx-sinx. Calculate the area in the first quadrant bounded by the x-axis, the y-axis and f?

Answer 1

that's the whole question, but i'm not given the limits or anything.

Answer 2

I think your condition is x>0 and y>0, and the boundaries is x,y and f(x)

Answer 3

ok, but what are the limits that i have to integrate?

Answer 4

I think there needs to be a domain for x the lower boundary is 0 and whats the upper boundary.. 2pi

Answer 5

graph it, I think the integration is from x=0 to where f(x) = 0, but as the way I graphed it here http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
Doesn't look like a finite answer if there is no stop point

Answer 6

yeah that's what i'm confused about
because it seems to be an indefinte integral...

Answer 7

well if its 1st quadrant the domain is (0, pi/4)

Answer 8

let y = 0

so solve cos(x) - sin(x) = 0

or cos(x) = sin(x)

this only occurs when x = pi/4

Answer 9

ok thanks.
cuz the answer is less than 1

Answer 10

seem like it's the first portion of the curve on the first quadrant, how about the rest?

Answer 11

but 1st quadrant may require you to integrate between (0 and pi/2)

Answer 12

ok thanks :D

Answer 13

so you will need to split it into 2 integrals as pi/4 to pi/2 is below the x-axis

so could use

\[\int\limits_{0}^{\frac{\pi}{4}} \cos(x) - \sin(x) dx + \int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} \cos(x) - \sin(x) dx \]

or

\[A = 2\int\limits_{0}^{\frac{\pi}{4}} \cos(x) - \sin(x) dx\]