Find the area of the region. (Round your answer to three decimal places.)

Question

between y = cos t and y = sin t for −π/2 ≤ t ≤ π/2

Answer 1

To get the algebraic (signed) area, just do

∫[-π/2,π/2] cos(t)-sin(t) dt = 2

But that value subtracts the area where cos < sin. If you want the physical area, you need to break up the region at π/4.

http://www.wolframalpha.com/input/?i=%E2%88%AB[-%CF%80%2F2%2C%CF%80%2F2]+%28cos%28t%29-sin%28t%29%29+dt

Answer 2

Would I then have to subtract the area sin(t)-cos(t)?

Answer 3

that would be correct, since then the sin curve is above the cos curve.

Answer 4

so would you subtract (-pi/2, pi/2) sin(t)-cos(t) on Wolframalpha?
I'm having trouble coming up with the value.