trig functions (1 Viewer)

[peppermint_stix]

ahhh i need help with integration of trig functions....this is from fitzpatrick exercise 17(g) q. 44.

find the points of intersection of the curves y=sin2@ and y=cos2@ for values of @ in the interval (0, pi) and calculate the measure of the area between the 2 curves in this interval.
note- (@ = theta)

the answer is (pi/8, 5pi/8) ; sqroot2

plzzz help!!!

 

[Heinz]

sin2@ = cos2@
tan2@ = 1 1st and 3rd quadrants
2@ = pi/4, pi + pi/4 = 5pi/4
therefore @ = pi/8, 5pi/8

you have to draw the two curves to see which one is the upper curve. Alternatively, sub in a value between the points of intersection to see which has the greater y value.

The area is the intergral from pi/8 to 5pi/8 of sin2@ - cos2@ d@. Solve that integral and you should get sqrt(2).

 

[redslert]

yep that's how i would do it too