Homework SourseFind the area that lies in the intersection of the circles r
Find the area that lies in the intersection of the circles r=10sin(t) and r=10cos(t) [t=theta]
Solution
these intersect at
sin t = cos t => t = pi/4 or 5pi/4
area b/w the curves = integ 10sin t - 10 cos t dt from pi/4 to 5pi/4
= 10 (- cos t - sint )) from pi/4 to 5pi/4
= -10 ( sin t + cos t) from pi/4 to 5pi/4
= -10( -1/2 - 1/2 - 1/2 - 1/2)
= 10 * 4/2
= 20 2 units
![Find the area that lies in the intersection of the circles r=10sin(t) and r=10cos(t) [t=theta]Solutionthese intersect at sin t = cos t => t = pi/4 or 5pi/4 a](/WebImages/43/find-the-area-that-lies-in-the-intersection-of-the-circles-r-1132950-1761605688-0.webp "Find the area that lies in the intersection of the circles r=10sin(t) and r=10cos(t) [t=theta]Solutionthese intersect at sin t = cos t => t = pi/4 or 5pi/4 a")
