## blackstreet23 one year ago Write down, but do not evaluate, an integral for the area of this shaded region.

1. blackstreet23

2. TheCatMan

im not that advanced in school yet i cant help here sorry

3. TheCatMan

@whpalmer4 can you help

4. anonymous

|dw:1442977155087:dw| This means the upper half of this region can be given by the double integral $\int_0^{\pi/4}\int_0^{\cos2 t}r\,dr\,dt=\frac{1}{2}\int_0^{\pi/4}\cos^2t\,dt$ How might you adjust the limits to account for the bottom half as well?

5. blackstreet23

i dont get it

6. blackstreet23

why pi/4?

7. blackstreet23

@SithsAndGiggles

8. blackstreet23

@Shalante

9. blackstreet23

@pooja195

10. anonymous

Your curve is defined by the function $$r(t)=\cos2t$$. When $$t=\dfrac{\pi}{4}$$, you have $r\left(\frac{\pi}{4}\right)=\cos\frac{2\pi}{4}=\cos\frac{\pi}{2}=0$ (You can check that $$r(t)\neq0$$ for values of $$t$$ between $$0$$ and $$t=\dfrac{\pi}{4}$$.)|dw:1443051824798:dw| As $$t$$ increases from $$0$$ to $$\dfrac{\pi}{4}$$, the curve is traced out in the direction indicated by the arrows.

11. blackstreet23

Thanks a lot !!! you are awesome :D